diff --git a/paddle/fluid/framework/operator.cc b/paddle/fluid/framework/operator.cc
index 42fbeb5d29ce4ac3a1498704b1fff88570c9c092..15777c287b42241350193583a21f3796febf5f02 100644
--- a/paddle/fluid/framework/operator.cc
+++ b/paddle/fluid/framework/operator.cc
@@ -1122,7 +1122,15 @@ static void CheckTensorNANOrInf(const std::string& op_type,
 
 bool OperatorWithKernel::SupportsMKLDNN(
     const proto::VarType::Type data_type) const {
-  auto& op_kernels = OperatorWithKernel::AllOpKernels().at(type_);
+  auto op_kernel_iter = OperatorWithKernel::AllOpKernels().find(type_);
+  if (op_kernel_iter == OperatorWithKernel::AllOpKernels().end()) {
+    VLOG(6) << "Warning: " << type_ << " don't find its MKLDNN Kernel in Fluid "
+                                       "Registered Kernels. And We don't "
+                                       "search its kernels in phi lib, "
+                                       "SupportsMKLDNN() return false.";
+    return false;
+  }
+  auto& op_kernels = op_kernel_iter->second;
   return std::any_of(op_kernels.begin(), op_kernels.end(),
                      [data_type](OpKernelMap::const_reference kern_pair) {
                        return platform::is_cpu_place(kern_pair.first.place_) &&
diff --git a/paddle/fluid/operators/activation_op.cc b/paddle/fluid/operators/activation_op.cc
index 845d0ed073b32cc136ec6b9d76c9e3073d7b051a..8f7b62a2c9d27b699688d53ff1545b80a8f4400c 100644
--- a/paddle/fluid/operators/activation_op.cc
+++ b/paddle/fluid/operators/activation_op.cc
@@ -1496,6 +1496,9 @@ REGISTER_ACTIVATION_OP(hard_sigmoid, HardSigmoid, HardSigmoidFunctor,
                        HardSigmoidGradFunctor);
 REGISTER_ACTIVATION_OP(logsigmoid, LogSigmoid, LogSigmoidFunctor,
                        LogSigmoidGradFunctor);
+REGISTER_ACTIVATION_OP(log2, Log2, Log2Functor, Log2GradFunctor);
+REGISTER_ACTIVATION_OP(log10, Log10, Log10Functor, Log10GradFunctor);
+REGISTER_ACTIVATION_OP(log1p, Log1p, Log1pFunctor, Log1pGradFunctor);
 
 /* ==========================    sigmoid register  =============================
  */
@@ -1867,15 +1870,6 @@ REGISTER_OPERATOR(
     ops::ActivationOpDoubleGrad<ops::LogGradGradFunctor<float>::FwdDeps()>,
     ops::ActivationDoubleGradOpInplaceInferer);
 
-REGISTER_ACTIVATION_CPU_KERNEL(log, Log, LogFunctor, LogGradFunctor);
-
-REGISTER_OP_CPU_KERNEL(
-    log_grad_grad, ops::LogDoubleGradKernel<plat::CPUDeviceContext,
-                                            ops::LogGradGradFunctor<float>>,
-    ops::LogDoubleGradKernel<plat::CPUDeviceContext,
-                             ops::LogGradGradFunctor<double>>,
-    ops::LogDoubleGradKernel<plat::CPUDeviceContext,
-                             ops::LogGradGradFunctor<plat::float16>>);
 /* ========================================================================== */
 
 /* ==========================  register checkpoint ===========================*/
diff --git a/paddle/fluid/operators/activation_op.h b/paddle/fluid/operators/activation_op.h
index f1984af6e15eac6682bd341f470727b899e82f3a..7db5675c16b2d3cc7df7176a40e2010355ebd37c 100644
--- a/paddle/fluid/operators/activation_op.h
+++ b/paddle/fluid/operators/activation_op.h
@@ -281,6 +281,11 @@ USE_PHI_DOUBLE_GRAD_FUNCTOR(Sigmoid)
 USE_PHI_TRIPLE_GRAD_FUNCTOR(Sigmoid)
 USE_PHI_FUNCTOR(LogSigmoid)
 USE_PHI_FUNCTOR(HardSigmoid)
+USE_PHI_FUNCTOR(Log)
+USE_PHI_DOUBLE_GRAD_FUNCTOR(Log)
+USE_PHI_FUNCTOR(Log2)
+USE_PHI_FUNCTOR(Log10)
+USE_PHI_FUNCTOR(Log1p)
 
 template <typename T>
 using ELUGradNegativeAlphaFunctor = phi::funcs::ELUGradNegativeAlphaFunctor<T>;
@@ -448,88 +453,6 @@ struct ReciprocalGradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
-// log(x) = natural logarithm of x
-template <typename T>
-struct LogFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out>
-  void operator()(Device d, X x, Out out) const {
-    out.device(d) = x.log();
-  }
-};
-
-template <typename T>
-struct LogGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out, typename dOut,
-            typename dX>
-  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
-    dx.device(d) = dout * (static_cast<T>(1) / x);
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
-// log2(x) = logarithm to the base 2 of the elements of x
-template <typename T>
-struct Log2Functor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out>
-  void operator()(Device d, X x, Out out) const {
-    out.device(d) = x.log() / static_cast<T>(log(2));
-  }
-};
-
-// the gradient of log2(x) is 1/(x*ln(2))
-template <typename T>
-struct Log2GradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out, typename dOut,
-            typename dX>
-  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
-    dx.device(d) = dout * static_cast<T>(1) / (x * static_cast<T>(log(2)));
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
-// log10(x) = logarithm to the base 10 of the elements of x
-template <typename T>
-struct Log10Functor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out>
-  void operator()(Device d, X x, Out out) const {
-    out.device(d) = x.log() / static_cast<T>(log(10));
-  }
-};
-
-// the gradient of log10(x) is 1/(x*ln(10))
-template <typename T>
-struct Log10GradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out, typename dOut,
-            typename dX>
-  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
-    dx.device(d) = dout * static_cast<T>(1) / (x * static_cast<T>(log(10)));
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
-// log1p(x) = natural logarithm of x+1
-template <typename T>
-struct Log1pFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out>
-  void operator()(Device d, X x, Out out) const {
-    out.device(d) = (static_cast<T>(1) + x).log();
-  }
-};
-
-template <typename T>
-struct Log1pGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Out, typename dOut,
-            typename dX>
-  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
-    dx.device(d) = dout * (static_cast<T>(1) / (x + static_cast<T>(1)));
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
 // square(x) = x^2
 template <typename T>
 struct SquareFunctor : public BaseActivationFunctor<T> {
@@ -1197,37 +1120,6 @@ class SquareDoubleGradKernel
   }
 };
 
-template <typename DeviceContext, typename Functor>
-class LogDoubleGradKernel
-    : public SquareDoubleGradKernel<DeviceContext, Functor> {};
-
-template <typename DeviceContext, typename Functor>
-class ELUDoubleGradKernel
-    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
- public:
-  using T = typename Functor::ELEMENT_TYPE;
-  void Compute(const framework::ExecutionContext& ctx) const override {
-    const framework::Tensor *X, *ddX, *dOut;
-    X = ddX = dOut = nullptr;
-    framework::Tensor *dX, *ddOut;
-    dX = ddOut = nullptr;
-
-    ExtractDoubleGradTensorWithInputDOut(ctx, &X, &ddX, &dX, &dOut, &ddOut);
-
-    if (dX) dX->mutable_data<T>(X->dims(), ctx.GetPlace());
-    if (ddOut) ddOut->mutable_data<T>(ctx.GetPlace());
-
-    auto& place = ctx.template device_context<DeviceContext>();
-
-    Functor functor;
-    auto attrs = functor.GetAttrs();
-    for (auto& attr : attrs) {
-      *attr.second = ctx.Attr<float>(attr.first);
-    }
-    functor(place, X, ddX, ddOut, dOut, dX);
-  }
-};
-
 template <typename DeviceContext, typename Functor>
 class CELUDoubleGradKernel
     : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
@@ -1522,36 +1414,6 @@ class LogitGradKernel : public framework::OpKernel<T> {
   }
 };
 
-template <typename T>
-struct LogGradGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device>
-  void operator()(const Device& dev, const framework::Tensor* X,
-                  const framework::Tensor* ddX, framework::Tensor* ddOut,
-                  const framework::Tensor* dOut, framework::Tensor* dX) const {
-    auto* d = dev.eigen_device();
-    auto ddx = framework::EigenVector<T>::Flatten(
-        GET_DATA_SAFELY(ddX, "Input", "DDX", "LogGradGrad"));
-    auto x = framework::EigenVector<T>::Flatten(
-        GET_DATA_SAFELY(X, "Input", "X", "LogGradGrad"));
-    // ddout = ddx / x; dx = -(dout / x) * (ddx / x)
-    // calculate dx first, so ddout can inplace ddx
-    if (dX) {
-      auto dout = framework::EigenVector<T>::Flatten(
-          GET_DATA_SAFELY(dOut, "Output", "DOut", "LogGradGrad"));
-      auto dx = framework::EigenVector<T>::Flatten(
-          GET_DATA_SAFELY(dX, "Output", "DX", "LogGradGrad"));
-      dx.device(*d) = dout * static_cast<T>(-1) * ddx / (x * x);
-    }
-    if (ddOut) {
-      auto ddout = framework::EigenVector<T>::Flatten(
-          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "LogGradGrad"));
-      ddout.device(*d) = ddx * static_cast<T>(1) / x;
-    }
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
 }  // namespace operators
 }  // namespace paddle
 
@@ -1560,9 +1422,6 @@ struct LogGradGradFunctor : public BaseActivationFunctor<T> {
   __macro(floor, Floor, FloorFunctor, ZeroGradFunctor);                      \
   __macro(round, Round, RoundFunctor, ZeroGradFunctor);                      \
   __macro(reciprocal, Reciprocal, ReciprocalFunctor, ReciprocalGradFunctor); \
-  __macro(log1p, Log1p, Log1pFunctor, Log1pGradFunctor);                     \
-  __macro(log2, Log2, Log2Functor, Log2GradFunctor);                         \
-  __macro(log10, Log10, Log10Functor, Log10GradFunctor);                     \
   __macro(soft_relu, SoftRelu, SoftReluFunctor, SoftReluGradFunctor);        \
   __macro(stanh, STanh, STanhFunctor, STanhGradFunctor);                     \
   __macro(softplus, Softplus, SoftplusFunctor, SoftplusGradFunctor);         \
diff --git a/paddle/fluid/operators/activation_op.kps b/paddle/fluid/operators/activation_op.kps
index 7c1b288080162e2a5bf847a795fc640ab5e5e4e1..bb08cee5bcde929f71415e5844a30c4d47f37b0a 100644
--- a/paddle/fluid/operators/activation_op.kps
+++ b/paddle/fluid/operators/activation_op.kps
@@ -131,27 +131,6 @@ struct CudaExpm1GradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
-template <typename T>
-struct CudaLogFunctor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-
-  // log(x) = log(x)
-  __device__ __forceinline__ T operator()(const T arg_x) const {
-    MPType x = static_cast<MPType>(arg_x);
-    return static_cast<T>(log(x));
-  }
-};
-
-template <typename T>
-struct CudaLogGradFunctor : public BaseActivationFunctor<T> {
-  // dx = dout / x
-  __device__ __forceinline__ T operator()(const T dout, const T x) const {
-    return dout / x;
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
 template <typename T>
 struct CudaSquareFunctor : public BaseActivationFunctor<T> {
   // square(x) = x * x
@@ -220,78 +199,6 @@ struct CudaRsqrtGradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
-template <typename T>
-struct CudaLog1pFunctor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-  MPType one = static_cast<MPType>(1.0f);
-
-  // log1p(x) = log(1 + x)
-  __device__ __forceinline__ T operator()(const T arg_x) const {
-    MPType x = static_cast<MPType>(arg_x);
-    return static_cast<T>(log(one + x));
-  }
-};
-
-template <typename T>
-struct CudaLog1pGradFunctor : public BaseActivationFunctor<T> {
-  T one = static_cast<T>(1.0f);
-
-  // dx = dout / (1 + x)
-  __device__ __forceinline__ T operator()(const T dout, const T x) const {
-    return dout / (one + x);
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
-template <typename T>
-struct CudaLog2Functor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-
-  // log2(x) = log2(x)
-  __device__ __forceinline__ T operator()(const T arg_x) const {
-    MPType x = static_cast<MPType>(arg_x);
-    return static_cast<T>(log2(x));
-  }
-};
-
-template <typename T>
-struct CudaLog2GradFunctor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-  T log_two = static_cast<T>(log(static_cast<MPType>(2.0f)));
-
-  // dx = dout / (x * log(2))
-  __device__ __forceinline__ T operator()(const T dout, const T x) const {
-    return dout / (x * log_two);
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
-template <typename T>
-struct CudaLog10Functor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-
-  // log10(x) = log10(x)
-  __device__ __forceinline__ T operator()(const T arg_x) const {
-    MPType x = static_cast<MPType>(arg_x);
-    return static_cast<T>(log10(x));
-  }
-};
-
-template <typename T>
-struct CudaLog10GradFunctor : public BaseActivationFunctor<T> {
-  using MPType = typename details::MPTypeTrait<T>::Type;
-  T log_ten = static_cast<T>(log(static_cast<MPType>(10.0f)));
-
-  // dx = dout / (x * log(10))
-  __device__ __forceinline__ T operator()(const T dout, const T x) const {
-    return dout / (x * log_ten);
-  }
-
-  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
-};
-
 template <typename T>
 struct CudaSoftReluFunctor : public BaseActivationFunctor<T> {
   using MPType = typename details::MPTypeTrait<T>::Type;
@@ -773,6 +680,10 @@ USE_PHI_FUNCTOR(CudaELU)
 USE_PHI_FUNCTOR(CudaSigmoid)
 USE_PHI_FUNCTOR(CudaLogSigmoid)
 USE_PHI_FUNCTOR(CudaHardSigmoid)
+USE_PHI_FUNCTOR(CudaLog)
+USE_PHI_FUNCTOR(CudaLog2)
+USE_PHI_FUNCTOR(CudaLog10)
+USE_PHI_FUNCTOR(CudaLog1p)
 
 template <typename T>
 using CudaELUGradNegativeAlphaFunctor =
@@ -975,18 +886,6 @@ REGISTER_OP_CUDA_KERNEL(
                                   ops::CudaExpm1GradFunctor<plat::float16>>);
 /* ========================================================================== */
 
-/* ==========================  Log register ==================================*/
-REGISTER_ACTIVATION_CUDA_KERNEL(log, Log, CudaLogFunctor, CudaLogGradFunctor);
-
-REGISTER_OP_CUDA_KERNEL(
-    log_grad_grad, ops::LogDoubleGradKernel<plat::CUDADeviceContext,
-                                            ops::LogGradGradFunctor<float>>,
-    ops::LogDoubleGradKernel<plat::CUDADeviceContext,
-                             ops::LogGradGradFunctor<double>>,
-    ops::LogDoubleGradKernel<plat::CUDADeviceContext,
-                             ops::LogGradGradFunctor<plat::float16>>);
-/* ========================================================================== */
-
 #define FOR_EACH_ACTIVATION_CUDA_OP(__macro)                                  \
   __macro(softshrink, SoftShrink, CudaSoftShrinkFunctor,                      \
           CudaSoftShrinkGradFunctor);                                         \
@@ -995,9 +894,6 @@ REGISTER_OP_CUDA_KERNEL(
   __macro(round, Round, CudaRoundFunctor, CudaZeroGradFunctor);               \
   __macro(reciprocal, Reciprocal, CudaReciprocalFunctor,                      \
           CudaReciprocalGradFunctor);                                         \
-  __macro(log1p, Log1p, CudaLog1pFunctor, CudaLog1pGradFunctor);              \
-  __macro(log2, Log2, CudaLog2Functor, CudaLog2GradFunctor);                  \
-  __macro(log10, Log10, CudaLog10Functor, CudaLog10GradFunctor);              \
   __macro(soft_relu, SoftRelu, CudaSoftReluFunctor, CudaSoftReluGradFunctor); \
   __macro(stanh, STanh, CudaSTanhFunctor, CudaSTanhGradFunctor);              \
   __macro(softplus, Softplus, CudaSoftplusFunctor, CudaSoftplusGradFunctor);  \
diff --git a/paddle/phi/kernels/activation_grad_kernel.h b/paddle/phi/kernels/activation_grad_kernel.h
index 241a80d85ead2d7bb6cd63105feb345c62a29a62..6ad28f348f22fc3c8bc6ba7e1ce2bb4d431971be 100644
--- a/paddle/phi/kernels/activation_grad_kernel.h
+++ b/paddle/phi/kernels/activation_grad_kernel.h
@@ -135,6 +135,14 @@ void SigmoidTripleGradKernel(const Context& dev_ctx,
                              DenseTensor* d_dout,
                              DenseTensor* d_ddx);
 
+template <typename T, typename Context>
+void LogDoubleGradKernel(const Context& dev_ctx,
+                         const DenseTensor& x,
+                         const DenseTensor& dout,
+                         const DenseTensor& ddx,
+                         DenseTensor* dx,
+                         DenseTensor* ddout);
+
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Cos);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Tan);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Acos);
@@ -149,6 +157,10 @@ DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Atanh);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(TanhShrink);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Silu);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(LogSigmoid);
+DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Log);
+DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Log2);
+DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Log10);
+DECLARE_ACTIVATION_GRAD_KERNEL_DEPX(Log1p);
 
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPOUT(Relu);
 DECLARE_ACTIVATION_GRAD_KERNEL_DEPOUT(Tanh);
diff --git a/paddle/phi/kernels/activation_kernel.h b/paddle/phi/kernels/activation_kernel.h
index dbc63a636edb188e4640fdd02895868034f1dd80..785d1089f06e8eece211a6d5978e1e0b1b67ba7f 100644
--- a/paddle/phi/kernels/activation_kernel.h
+++ b/paddle/phi/kernels/activation_kernel.h
@@ -56,6 +56,10 @@ DECLARE_ACTIVATION_KERNEL(TanhShrink)
 DECLARE_ACTIVATION_KERNEL(Silu)
 DECLARE_ACTIVATION_KERNEL(Sigmoid)
 DECLARE_ACTIVATION_KERNEL(LogSigmoid)
+DECLARE_ACTIVATION_KERNEL(Log)
+DECLARE_ACTIVATION_KERNEL(Log2)
+DECLARE_ACTIVATION_KERNEL(Log10)
+DECLARE_ACTIVATION_KERNEL(Log1p)
 
 DECLARE_ACTIVATION_KERNEL_WITH_ONE_ATTRS(LeakyRelu, alpha)
 DECLARE_ACTIVATION_KERNEL_WITH_ONE_ATTRS(ThresholdedRelu, threshold)
diff --git a/paddle/phi/kernels/cpu/activation_grad_kernel.cc b/paddle/phi/kernels/cpu/activation_grad_kernel.cc
index c582261596221f4db8bd03599386082cee909096..0776e570e9cd35be4a0f7d10c8fb4dd40aa07171 100644
--- a/paddle/phi/kernels/cpu/activation_grad_kernel.cc
+++ b/paddle/phi/kernels/cpu/activation_grad_kernel.cc
@@ -121,6 +121,10 @@ DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Atanh, AtanhGradFunctor);
 DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(TanhShrink, TanhShrinkGradFunctor);
 DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Silu, SiluGradFunctor);
 DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(LogSigmoid, LogSigmoidGradFunctor);
+DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Log, LogGradFunctor);
+DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Log2, Log2GradFunctor);
+DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Log10, Log10GradFunctor);
+DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPX(Log1p, Log1pGradFunctor);
 
 DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPOUT(Relu, ReluGradFunctor);
 DEFINE_CPU_ACTIVATION_GRAD_KERNEL_DEPOUT(Tanh, TanhGradFunctor);
@@ -233,3 +237,8 @@ PD_REGISTER_ACTIVATION_GRAD_KERNEL(sigmoid_double_grad, SigmoidDoubleGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(sigmoid_triple_grad, SigmoidTripleGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(hard_sigmoid_grad, HardSigmoidGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(logsigmoid_grad, LogSigmoidGradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log_grad, LogGradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log2_grad, Log2GradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log10_grad, Log10GradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log1p_grad, Log1pGradKernel)
+PD_REGISTER_ACTIVATION_DOUBLE_GRAD_KERNEL(log_double_grad, LogDoubleGradKernel)
diff --git a/paddle/phi/kernels/cpu/activation_kernel.cc b/paddle/phi/kernels/cpu/activation_kernel.cc
index 1d7b77ea4445f494105d4c23516f31f349847089..c8709261d2cb0b162306b0c52d5dfefd6f09ef52 100644
--- a/paddle/phi/kernels/cpu/activation_kernel.cc
+++ b/paddle/phi/kernels/cpu/activation_kernel.cc
@@ -74,6 +74,10 @@ DEFINE_CPU_ACTIVATION_KERNEL(TanhShrink, TanhShrinkFunctor)
 DEFINE_CPU_ACTIVATION_KERNEL(Silu, SiluFunctor)
 DEFINE_CPU_ACTIVATION_KERNEL(Sigmoid, SigmoidFunctor)
 DEFINE_CPU_ACTIVATION_KERNEL(LogSigmoid, LogSigmoidFunctor)
+DEFINE_CPU_ACTIVATION_KERNEL(Log, LogFunctor)
+DEFINE_CPU_ACTIVATION_KERNEL(Log2, Log2Functor)
+DEFINE_CPU_ACTIVATION_KERNEL(Log10, Log10Functor)
+DEFINE_CPU_ACTIVATION_KERNEL(Log1p, Log1pFunctor)
 
 DEFINE_CPU_ACT_KERNEL_WITH_ONE_ATTRS(LeakyRelu, LeakyReluFunctor, alpha)
 DEFINE_CPU_ACT_KERNEL_WITH_ONE_ATTRS(ThresholdedRelu,
@@ -118,3 +122,7 @@ PD_REGISTER_ACTIVATION_KERNEL(silu, SiluKernel)
 PD_REGISTER_ACTIVATION_KERNEL(sigmoid, SigmoidKernel)
 PD_REGISTER_ACTIVATION_KERNEL(logsigmoid, LogSigmoidKernel)
 PD_REGISTER_ACTIVATION_KERNEL(hard_sigmoid, HardSigmoidKernel)
+PD_REGISTER_ACTIVATION_KERNEL(log, LogKernel)
+PD_REGISTER_ACTIVATION_KERNEL(log2, Log2Kernel)
+PD_REGISTER_ACTIVATION_KERNEL(log10, Log10Kernel)
+PD_REGISTER_ACTIVATION_KERNEL(log1p, Log1pKernel)
diff --git a/paddle/phi/kernels/funcs/activation_functor.h b/paddle/phi/kernels/funcs/activation_functor.h
index 6c5ffbd06e3a435d9568a6c4717d8ce83b5aec00..6e536bd00a4a12fc2e4034920c344993f54f447b 100644
--- a/paddle/phi/kernels/funcs/activation_functor.h
+++ b/paddle/phi/kernels/funcs/activation_functor.h
@@ -1223,6 +1223,133 @@ struct HardSigmoidGradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
+// log(x) = natural logarithm of x
+template <typename T>
+struct LogFunctor : public BaseActivationFunctor<T> {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.log();
+  }
+};
+
+template <typename T>
+struct LogGradFunctor : public BaseActivationFunctor<T> {
+  template <typename Device,
+            typename X,
+            typename Out,
+            typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (static_cast<T>(1) / x);
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+// log2(x) = logarithm to the base 2 of the elements of x
+template <typename T>
+struct Log2Functor : public BaseActivationFunctor<T> {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.log() / static_cast<T>(log(2));
+  }
+};
+
+// the gradient of log2(x) is 1/(x*ln(2))
+template <typename T>
+struct Log2GradFunctor : public BaseActivationFunctor<T> {
+  template <typename Device,
+            typename X,
+            typename Out,
+            typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * static_cast<T>(1) / (x * static_cast<T>(log(2)));
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+// log10(x) = logarithm to the base 10 of the elements of x
+template <typename T>
+struct Log10Functor : public BaseActivationFunctor<T> {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.log() / static_cast<T>(log(10));
+  }
+};
+
+// the gradient of log10(x) is 1/(x*ln(10))
+template <typename T>
+struct Log10GradFunctor : public BaseActivationFunctor<T> {
+  template <typename Device,
+            typename X,
+            typename Out,
+            typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * static_cast<T>(1) / (x * static_cast<T>(log(10)));
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+// log1p(x) = natural logarithm of x+1
+template <typename T>
+struct Log1pFunctor : public BaseActivationFunctor<T> {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = (static_cast<T>(1) + x).log();
+  }
+};
+
+template <typename T>
+struct Log1pGradFunctor : public BaseActivationFunctor<T> {
+  template <typename Device,
+            typename X,
+            typename Out,
+            typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (static_cast<T>(1) / (x + static_cast<T>(1)));
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+template <typename T>
+struct LogGradGradFunctor : public BaseActivationFunctor<T> {
+  template <typename Device>
+  void operator()(const Device& dev,
+                  const DenseTensor* X,
+                  const DenseTensor* ddX,
+                  DenseTensor* ddOut,
+                  const DenseTensor* dOut,
+                  DenseTensor* dX) const {
+    auto* d = dev.eigen_device();
+    auto ddx = EigenVector<T>::Flatten(
+        GET_DATA_SAFELY(ddX, "Input", "DDX", "LogGradGrad"));
+    auto x = EigenVector<T>::Flatten(
+        GET_DATA_SAFELY(X, "Input", "X", "LogGradGrad"));
+    // ddout = ddx / x; dx = -(dout / x) * (ddx / x)
+    // calculate dx first, so ddout can inplace ddx
+    if (dX) {
+      auto dout = EigenVector<T>::Flatten(
+          GET_DATA_SAFELY(dOut, "Output", "DOut", "LogGradGrad"));
+      auto dx = EigenVector<T>::Flatten(
+          GET_DATA_SAFELY(dX, "Output", "DX", "LogGradGrad"));
+      dx.device(*d) = dout * static_cast<T>(-1) * ddx / (x * x);
+    }
+    if (ddOut) {
+      auto ddout = EigenVector<T>::Flatten(
+          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "LogGradGrad"));
+      ddout.device(*d) = ddx * static_cast<T>(1) / x;
+    }
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
 #if defined(__NVCC__) || defined(__HIPCC__) || defined(__xpu__)
 template <typename T>
 struct CudaReluFunctor : public BaseActivationFunctor<T> {
@@ -1970,6 +2097,99 @@ struct CudaHardSigmoidGradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
+template <typename T>
+struct CudaLogFunctor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+
+  // log(x) = log(x)
+  __device__ __forceinline__ T operator()(const T arg_x) const {
+    MPType x = static_cast<MPType>(arg_x);
+    return static_cast<T>(log(x));
+  }
+};
+
+template <typename T>
+struct CudaLogGradFunctor : public BaseActivationFunctor<T> {
+  // dx = dout / x
+  __device__ __forceinline__ T operator()(const T dout, const T x) const {
+    return dout / x;
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+template <typename T>
+struct CudaLog1pFunctor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+  MPType one = static_cast<MPType>(1.0f);
+
+  // log1p(x) = log(1 + x)
+  __device__ __forceinline__ T operator()(const T arg_x) const {
+    MPType x = static_cast<MPType>(arg_x);
+    return static_cast<T>(log(one + x));
+  }
+};
+
+template <typename T>
+struct CudaLog1pGradFunctor : public BaseActivationFunctor<T> {
+  T one = static_cast<T>(1.0f);
+
+  // dx = dout / (1 + x)
+  __device__ __forceinline__ T operator()(const T dout, const T x) const {
+    return dout / (one + x);
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+template <typename T>
+struct CudaLog2Functor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+
+  // log2(x) = log2(x)
+  __device__ __forceinline__ T operator()(const T arg_x) const {
+    MPType x = static_cast<MPType>(arg_x);
+    return static_cast<T>(log2(x));
+  }
+};
+
+template <typename T>
+struct CudaLog2GradFunctor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+  T log_two = static_cast<T>(log(static_cast<MPType>(2.0f)));
+
+  // dx = dout / (x * log(2))
+  __device__ __forceinline__ T operator()(const T dout, const T x) const {
+    return dout / (x * log_two);
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
+template <typename T>
+struct CudaLog10Functor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+
+  // log10(x) = log10(x)
+  __device__ __forceinline__ T operator()(const T arg_x) const {
+    MPType x = static_cast<MPType>(arg_x);
+    return static_cast<T>(log10(x));
+  }
+};
+
+template <typename T>
+struct CudaLog10GradFunctor : public BaseActivationFunctor<T> {
+  using MPType = typename phi::dtype::MPTypeTrait<T>::Type;
+  T log_ten = static_cast<T>(log(static_cast<MPType>(10.0f)));
+
+  // dx = dout / (x * log(10))
+  __device__ __forceinline__ T operator()(const T dout, const T x) const {
+    return dout / (x * log_ten);
+  }
+
+  static constexpr ActBwdOpFwdDeps FwdDeps() { return ActBwdOpFwdDeps::kDepX; }
+};
+
 #endif
 
 }  // namespace funcs
diff --git a/paddle/phi/kernels/gpu/activation_grad_kernel.cu b/paddle/phi/kernels/gpu/activation_grad_kernel.cu
index c912d0c4686ff3fee88925f4d7121f38f24a5485..3cc41555a898b041921aecea309eb6d97d58a0ba 100644
--- a/paddle/phi/kernels/gpu/activation_grad_kernel.cu
+++ b/paddle/phi/kernels/gpu/activation_grad_kernel.cu
@@ -177,6 +177,10 @@ DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Atanh, CudaAtanhGradFunctor);
 DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(TanhShrink, CudaTanhShrinkGradFunctor);
 DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Silu, CudaSiluGradFunctor);
 DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(LogSigmoid, CudaLogSigmoidGradFunctor);
+DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Log, CudaLogGradFunctor);
+DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Log2, CudaLog2GradFunctor);
+DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Log10, CudaLog10GradFunctor);
+DEFINE_GPU_ACTIVATION_GRAD_KERNEL_DEPX(Log1p, CudaLog1pGradFunctor);
 
 DEFINE_GPU_ACT_GRAD_KERNEL_WITH_ONE_ATTRS_DEPX(LeakyRelu,
                                                CudaLeakyReluGradFunctor,
@@ -300,3 +304,14 @@ PD_REGISTER_ACTIVATION_GRAD_KERNEL(sigmoid_double_grad, SigmoidDoubleGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(sigmoid_triple_grad, SigmoidTripleGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(hard_sigmoid_grad, HardSigmoidGradKernel)
 PD_REGISTER_ACTIVATION_GRAD_KERNEL(logsigmoid_grad, LogSigmoidGradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log_grad, LogGradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log2_grad, Log2GradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log10_grad, Log10GradKernel)
+PD_REGISTER_ACTIVATION_GRAD_KERNEL(log1p_grad, Log1pGradKernel)
+PD_REGISTER_KERNEL(log_double_grad,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::LogDoubleGradKernel,
+                   float,
+                   double,
+                   phi::dtype::float16) {}
diff --git a/paddle/phi/kernels/gpu/activation_kernel.cu b/paddle/phi/kernels/gpu/activation_kernel.cu
index 6b598c764debb059072ba3ae3ac90e6985479133..fb4e2e07b21cbed384248fd8400a04a6e1965320 100644
--- a/paddle/phi/kernels/gpu/activation_kernel.cu
+++ b/paddle/phi/kernels/gpu/activation_kernel.cu
@@ -19,7 +19,7 @@ limitations under the License. */
 #include "paddle/phi/common/float16.h"
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/funcs/elementwise_base.h"
-#include "paddle/phi/kernels/impl/activation_grad_impl.h"
+#include "paddle/phi/kernels/impl/activation_impl.h"
 
 #include "paddle/fluid/platform/device/gpu/gpu_device_function.h"
 
@@ -93,6 +93,10 @@ DEFINE_GPU_ACTIVATION_KERNEL(TanhShrink, CudaTanhShrinkFunctor)
 DEFINE_GPU_ACTIVATION_KERNEL(Silu, CudaSiluFunctor)
 DEFINE_GPU_ACTIVATION_KERNEL(Sigmoid, CudaSigmoidFunctor)
 DEFINE_GPU_ACTIVATION_KERNEL(LogSigmoid, CudaLogSigmoidFunctor)
+DEFINE_GPU_ACTIVATION_KERNEL(Log, CudaLogFunctor)
+DEFINE_GPU_ACTIVATION_KERNEL(Log2, CudaLog2Functor)
+DEFINE_GPU_ACTIVATION_KERNEL(Log10, CudaLog10Functor)
+DEFINE_GPU_ACTIVATION_KERNEL(Log1p, CudaLog1pFunctor)
 
 DEFINE_GPU_ACT_KERNEL_WITH_ONE_ATTRS(LeakyRelu, CudaLeakyReluFunctor, alpha)
 DEFINE_GPU_ACT_KERNEL_WITH_ONE_ATTRS(ThresholdedRelu,
@@ -164,3 +168,7 @@ PD_REGISTER_ACTIVATION_KERNEL(silu, SiluKernel)
 PD_REGISTER_ACTIVATION_KERNEL(sigmoid, SigmoidKernel)
 PD_REGISTER_ACTIVATION_KERNEL(logsigmoid, LogSigmoidKernel)
 PD_REGISTER_ACTIVATION_KERNEL(hard_sigmoid, HardSigmoidKernel)
+PD_REGISTER_ACTIVATION_KERNEL(log, LogKernel)
+PD_REGISTER_ACTIVATION_KERNEL(log2, Log2Kernel)
+PD_REGISTER_ACTIVATION_KERNEL(log10, Log10Kernel)
+PD_REGISTER_ACTIVATION_KERNEL(log1p, Log1pKernel)
diff --git a/paddle/phi/kernels/impl/activation_grad_impl.h b/paddle/phi/kernels/impl/activation_grad_impl.h
index 7d6b6dc72ea60214ff4c9974b4ff885feecb5822..7ef8a0887c75cce8be9618593073e84089739c30 100644
--- a/paddle/phi/kernels/impl/activation_grad_impl.h
+++ b/paddle/phi/kernels/impl/activation_grad_impl.h
@@ -275,4 +275,22 @@ void SigmoidTripleGradKernel(const Context& dev_ctx,
           d_ddx);
 }
 
+template <typename T, typename Context>
+void LogDoubleGradKernel(const Context& dev_ctx,
+                         const DenseTensor& x,
+                         const DenseTensor& dout,
+                         const DenseTensor& ddx,
+                         DenseTensor* dx,
+                         DenseTensor* ddout) {
+  if (dx) {
+    dx->Resize(x.dims());
+    dev_ctx.template Alloc<T>(dx);
+  }
+  if (ddout) {
+    dev_ctx.template Alloc<T>(ddout);
+  }
+  funcs::LogGradGradFunctor<T> functor;
+  functor(dev_ctx, &x, &ddx, ddout, &dout, dx);
+}
+
 }  // namespace phi
diff --git a/paddle/phi/ops/compat/activation_sig.cc b/paddle/phi/ops/compat/activation_sig.cc
index 7ae0dc45c5e1be09a31821c171b84fbb47fe1c9e..8b4884e35b608c1d60645e5d2b59131f240d8be3 100644
--- a/paddle/phi/ops/compat/activation_sig.cc
+++ b/paddle/phi/ops/compat/activation_sig.cc
@@ -57,6 +57,10 @@ DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(HardShrink, "hard_shrink", "threshold");
 DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(TanhShrink, "tanh_shrink", );  // NOLINT
 DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(Silu, "silu", );               // NOLINT
 DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(LogSigmoid, "logsigmoid", );   // NOLINT
+DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(Log, "log", );                 // NOLINT
+DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(Log2, "log2", );               // NOLINT
+DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(Log10, "log10", );             // NOLINT
+DEFINE_ACT_GRAD_DEPX_OP_ARGMAP(Log1p, "log1p", );             // NOLINT
 
 DEFINE_ACT_GRAD_DEPOUT_OP_ARGMAP(Relu, "relu", );        // NOLINT
 DEFINE_ACT_GRAD_DEPOUT_OP_ARGMAP(Tanh, "tanh", );        // NOLINT
@@ -125,6 +129,12 @@ KernelSignature EluDoubleGradOpArgumentMapping(
       "elu_double_grad", {"X", "DOut", "DDX"}, {"alpha"}, {"DX", "DDOut"});
 }
 
+KernelSignature LogDoubleGradOpArgumentMapping(
+    const ArgumentMappingContext& ctx) {
+  return KernelSignature(
+      "log_double_grad", {"X", "DOut", "DDX"}, {}, {"DX", "DDOut"});
+}
+
 }  // namespace phi
 
 PD_REGISTER_BASE_KERNEL_NAME(relu_grad_grad, relu_double_grad);
@@ -134,6 +144,7 @@ PD_REGISTER_BASE_KERNEL_NAME(softshrink, soft_shrink);
 PD_REGISTER_BASE_KERNEL_NAME(softshrink_grad, soft_shrink_grad);
 PD_REGISTER_BASE_KERNEL_NAME(elu_grad_grad, elu_double_grad);
 PD_REGISTER_BASE_KERNEL_NAME(sigmoid_grad_grad, sigmoid_double_grad);
+PD_REGISTER_BASE_KERNEL_NAME(log_grad_grad, log_double_grad);
 
 PD_REGISTER_ARG_MAPPING_FN(cos_grad, phi::CosGradOpArgumentMapping);
 PD_REGISTER_ARG_MAPPING_FN(tan_grad, phi::TanGradOpArgumentMapping);
@@ -181,3 +192,8 @@ PD_REGISTER_ARG_MAPPING_FN(logsigmoid_grad,
                            phi::LogSigmoidGradOpArgumentMapping);
 PD_REGISTER_ARG_MAPPING_FN(hard_sigmoid_grad,
                            phi::HardSigmoidGradOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(log_grad, phi::LogGradOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(log_grad_grad, phi::LogDoubleGradOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(log2_grad, phi::Log2GradOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(log10_grad, phi::Log10GradOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(log1p_grad, phi::Log1pGradOpArgumentMapping);