diff --git a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
--- a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
+++ b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
@@ -315,6 +315,28 @@
   }
 };
 
+struct LogOpConversion : public OpConversionPattern<complex::LogOp> {
+  using OpConversionPattern<complex::LogOp>::OpConversionPattern;
+
+  LogicalResult
+  matchAndRewrite(complex::LogOp op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    complex::LogOp::Adaptor transformed(operands);
+    auto type = transformed.complex().getType().cast<ComplexType>();
+    auto elementType = type.getElementType().cast<FloatType>();
+    mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
+
+    Value abs = b.create<complex::AbsOp>(elementType, transformed.complex());
+    Value resultReal = b.create<math::LogOp>(elementType, abs);
+    Value real = b.create<complex::ReOp>(elementType, transformed.complex());
+    Value imag = b.create<complex::ImOp>(elementType, transformed.complex());
+    Value resultImag = b.create<math::Atan2Op>(elementType, imag, real);
+    rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
+                                                   resultImag);
+    return success();
+  }
+};
+
 struct NegOpConversion : public OpConversionPattern<complex::NegOp> {
   using OpConversionPattern<complex::NegOp>::OpConversionPattern;
 
@@ -374,6 +396,7 @@
       ComparisonOpConversion<complex::NotEqualOp, CmpFPredicate::UNE>,
       DivOpConversion,
       ExpOpConversion,
+      LogOpConversion,
       NegOpConversion,
       SignOpConversion>(patterns.getContext());
   // clang-format on
@@ -396,8 +419,8 @@
   target.addLegalDialect<StandardOpsDialect, math::MathDialect,
                          complex::ComplexDialect>();
   target.addIllegalOp<complex::AbsOp, complex::DivOp, complex::EqualOp,
-                      complex::ExpOp, complex::NotEqualOp, complex::NegOp,
-                      complex::SignOp>();
+                      complex::ExpOp, complex::LogOp, complex::NotEqualOp,
+                      complex::NegOp, complex::SignOp>();
   if (failed(applyPartialConversion(function, target, std::move(patterns))))
     signalPassFailure();
 }
diff --git a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
--- a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
@@ -154,6 +154,25 @@
 // CHECK: %[[RESULT:.*]] = complex.create %[[RESULT_REAL]], %[[RESULT_IMAG]] : complex<f32>
 // CHECK: return %[[RESULT]] : complex<f32>
 
+// CHECK-LABEL: func @complex_log
+// CHECK-SAME: %[[ARG:.*]]: complex<f32>
+func @complex_log(%arg: complex<f32>) -> complex<f32> {
+  %log = complex.log %arg: complex<f32>
+  return %log : complex<f32>
+}
+// CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
+// CHECK: %[[SQR_REAL:.*]] = mulf %[[REAL]], %[[REAL]] : f32
+// CHECK: %[[SQR_IMAG:.*]] = mulf %[[IMAG]], %[[IMAG]] : f32
+// CHECK: %[[SQ_NORM:.*]] = addf %[[SQR_REAL]], %[[SQR_IMAG]] : f32
+// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] : f32
+// CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
+// CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
+// CHECK: %[[RESULT_IMAG:.*]] = math.atan2 %[[IMAG2]], %[[REAL2]] : f32
+// CHECK: %[[RESULT:.*]] = complex.create %[[RESULT_REAL]], %[[RESULT_IMAG]] : complex<f32>
+// CHECK: return %[[RESULT]] : complex<f32>
+
 // CHECK-LABEL: func @complex_neg
 // CHECK-SAME: %[[ARG:.*]]: complex<f32>
 func @complex_neg(%arg: complex<f32>) -> complex<f32> {