diff --git a/mlx/backend/cpu/simd/base_simd.h b/mlx/backend/cpu/simd/base_simd.h
index bc416fc22..7e82a4d56 100644
--- a/mlx/backend/cpu/simd/base_simd.h
+++ b/mlx/backend/cpu/simd/base_simd.h
@@ -87,7 +87,6 @@ DEFAULT_UNARY(cosh, std::cosh)
 DEFAULT_UNARY(expm1, std::expm1)
 DEFAULT_UNARY(floor, std::floor)
 DEFAULT_UNARY(log, std::log)
-DEFAULT_UNARY(log2, std::log2)
 DEFAULT_UNARY(log10, std::log10)
 DEFAULT_UNARY(log1p, std::log1p)
 DEFAULT_UNARY(sinh, std::sinh)
@@ -95,6 +94,17 @@ DEFAULT_UNARY(sqrt, std::sqrt)
 DEFAULT_UNARY(tan, std::tan)
 DEFAULT_UNARY(tanh, std::tanh)
 
+template <typename T>
+Simd<T, 1> log2(Simd<T, 1> in) {
+  if constexpr (is_complex<T>) {
+    auto out = std::log(in.value);
+    auto scale = decltype(out.real())(M_LN2);
+    return Simd<T, 1>{T{out.real() / scale, out.imag() / scale}};
+  } else {
+    return Simd<T, 1>{std::log2(in.value)};
+  }
+}
+
 template <typename T>
 Simd<T, 1> operator~(Simd<T, 1> in) {
   return ~in.value;
diff --git a/mlx/backend/metal/kernels/unary.metal b/mlx/backend/metal/kernels/unary.metal
index 82692c8e5..2209b0665 100644
--- a/mlx/backend/metal/kernels/unary.metal
+++ b/mlx/backend/metal/kernels/unary.metal
@@ -73,6 +73,9 @@ instantiate_unary_all_same(Conjugate, complex64, complex64_t)
 instantiate_unary_all_same(Cos, complex64, complex64_t)
 instantiate_unary_all_same(Cosh, complex64, complex64_t)
 instantiate_unary_all_same(Exp, complex64, complex64_t)
+instantiate_unary_all_same(Log, complex64, complex64_t)
+instantiate_unary_all_same(Log2, complex64, complex64_t)
+instantiate_unary_all_same(Log10, complex64, complex64_t)
 instantiate_unary_all_same(Negative, complex64, complex64_t)
 instantiate_unary_all_same(Sign, complex64, complex64_t)
 instantiate_unary_all_same(Sin, complex64, complex64_t)
diff --git a/mlx/backend/metal/kernels/unary_ops.h b/mlx/backend/metal/kernels/unary_ops.h
index ceed3efe5..52e126b40 100644
--- a/mlx/backend/metal/kernels/unary_ops.h
+++ b/mlx/backend/metal/kernels/unary_ops.h
@@ -257,6 +257,13 @@ struct Log {
   T operator()(T x) {
     return metal::precise::log(x);
   };
+
+  template <>
+  complex64_t operator()(complex64_t x) {
+    auto r = metal::precise::log(Abs{}(x).real);
+    auto i = metal::precise::atan2(x.imag, x.real);
+    return {r, i};
+  };
 };
 
 struct Log2 {
@@ -264,6 +271,12 @@ struct Log2 {
   T operator()(T x) {
     return metal::precise::log2(x);
   };
+
+  template <>
+  complex64_t operator()(complex64_t x) {
+    auto y = Log{}(x);
+    return {y.real / M_LN2_F, y.imag / M_LN2_F};
+  };
 };
 
 struct Log10 {
@@ -271,6 +284,12 @@ struct Log10 {
   T operator()(T x) {
     return metal::precise::log10(x);
   };
+
+  template <>
+  complex64_t operator()(complex64_t x) {
+    auto y = Log{}(x);
+    return {y.real / M_LN10_F, y.imag / M_LN10_F};
+  };
 };
 
 struct Log1p {
diff --git a/python/tests/test_ops.py b/python/tests/test_ops.py
index 302c017a0..d7c79d9db 100644
--- a/python/tests/test_ops.py
+++ b/python/tests/test_ops.py
@@ -845,6 +845,11 @@ class TestOps(mlx_tests.MLXTestCase):
 
         self.assertTrue(np.allclose(result, expected))
 
+        a = mx.array(1.0) + 1j * mx.array(2.0)
+        result = mx.log(a)
+        expected = np.log(np.array(a))
+        self.assertTrue(np.allclose(result, expected))
+
     def test_log2(self):
         a = mx.array([0.5, 1, 2, 10, 16])
         result = mx.log2(a)
@@ -852,6 +857,11 @@ class TestOps(mlx_tests.MLXTestCase):
 
         self.assertTrue(np.allclose(result, expected))
 
+        a = mx.array(1.0) + 1j * mx.array(2.0)
+        result = mx.log2(a)
+        expected = np.log2(np.array(a))
+        self.assertTrue(np.allclose(result, expected))
+
     def test_log10(self):
         a = mx.array([0.1, 1, 10, 20, 100])
         result = mx.log10(a)
@@ -859,6 +869,11 @@ class TestOps(mlx_tests.MLXTestCase):
 
         self.assertTrue(np.allclose(result, expected))
 
+        a = mx.array(1.0) + 1j * mx.array(2.0)
+        result = mx.log10(a)
+        expected = np.log10(np.array(a))
+        self.assertTrue(np.allclose(result, expected))
+
     def test_exp(self):
         a = mx.array([0, 0.5, -0.5, 5])
         result = mx.exp(a)