diff --git a/library/core/src/num/uint_macros.rs b/library/core/src/num/uint_macros.rs
index d68c7be9865b1..3184d13d25cfe 100644
--- a/library/core/src/num/uint_macros.rs
+++ b/library/core/src/num/uint_macros.rs
@@ -1571,9 +1571,14 @@ macro_rules! uint_impl {
             // applied by the compiler. If you want those specific bases,
             // use `.checked_ilog2()` or `.checked_ilog10()` directly.
             if core::intrinsics::is_val_statically_known(base) {
-                if base == 2 {
-                    return self.checked_ilog2();
-                } else if base == 10 {
+                // change of base:
+                // if base == 2 ** k, then
+                // log(base, n) == log(2, n) / k
+                if base.is_power_of_two() && base > 1 {
+                    let k = base.ilog2();
+                    return Some(try_opt!(self.checked_ilog2()) / k);
+                }
+                if base == 10 {
                     return self.checked_ilog10();
                 }
             }
@@ -3309,6 +3314,18 @@ macro_rules! uint_impl {
             let mut base = self;
             let mut acc = 1;
 
+            if intrinsics::is_val_statically_known(base) {
+                // change of base:
+                // if base == 2 ** k, then
+                //    (2 ** k) ** n
+                // == 2 ** (k * n)
+                // == 1 << (k * n)
+                if base.is_power_of_two() {
+                    let k = base.ilog2();
+                    return 1 << (k * exp)
+                }
+            }
+
             if intrinsics::is_val_statically_known(exp) {
                 while exp > 1 {
                     if (exp & 1) == 1 {
diff --git a/tests/codegen-llvm/ilog_known_base.rs b/tests/codegen-llvm/ilog_known_base.rs
new file mode 100644
index 0000000000000..3f0cdd551c28b
--- /dev/null
+++ b/tests/codegen-llvm/ilog_known_base.rs
@@ -0,0 +1,36 @@
+//@ compile-flags: -Copt-level=3
+// Test that `checked_ilog` can use a faster implementation when `base` is a
+// known power of two
+
+#![crate_type = "lib"]
+
+// CHECK-LABEL: @checked_ilog2
+#[no_mangle]
+pub fn checked_ilog2(val: u32) -> Option<u32> {
+    // CHECK: %[[ICMP:.+]] = icmp ne i32 %val, 0
+    // CHECK: %[[CTZ:.+]] = tail call range(i32 0, 33) i32 @llvm.ctlz.i32(i32 %val, i1 true)
+    // CHECK: %[[LOG2:.+]] = xor i32 %[[CTZ]], 31
+    val.checked_ilog(2)
+}
+
+// log(4, x) == log(2, x) / 2
+// CHECK-LABEL: @checked_ilog4
+#[no_mangle]
+pub fn checked_ilog4(val: u32) -> Option<u32> {
+    // CHECK: %[[ICMP:.+]] = icmp ne i32 %val, 0
+    // CHECK: %[[CTZ:.+]] = tail call range(i32 0, 33) i32 @llvm.ctlz.i32(i32 %val, i1 true)
+    // CHECK: %[[DIV2:.+]] = lshr i32 %[[CTZ]], 1
+    // CHECK: %[[LOG4:.+]] = xor i32 %[[DIV2]], 15
+    val.checked_ilog(4)
+}
+
+// log(16, x) == log(2, x) / 4
+// CHECK-LABEL: @checked_ilog16
+#[no_mangle]
+pub fn checked_ilog16(val: u32) -> Option<u32> {
+    // CHECK: %[[ICMP:.+]] = icmp ne i32 %val, 0
+    // CHECK: %[[CTZ:.+]] = tail call range(i32 0, 33) i32 @llvm.ctlz.i32(i32 %val, i1 true)
+    // CHECK: %[[DIV4:.+]] = lshr i32 %[[CTZ]], 2
+    // CHECK: %[[LOG16:.+]] = xor i32 %[[DIV2]], 7
+    val.checked_ilog(16)
+}
diff --git a/tests/codegen-llvm/pow_known_base.rs b/tests/codegen-llvm/pow_known_base.rs
new file mode 100644
index 0000000000000..34a56a74c848d
--- /dev/null
+++ b/tests/codegen-llvm/pow_known_base.rs
@@ -0,0 +1,36 @@
+//@ compile-flags: -Copt-level=3
+// Test that `pow` can use a faster implementation when `base` is a
+// known power of two
+
+#![crate_type = "lib"]
+
+// CHECK-LABEL: @pow2
+#[no_mangle]
+pub fn pow2(exp: u32) -> u32 {
+    // CHECK: %[[SHIFT_AMOUNT:.+]] = and i32 %exp, 31
+    // CHECK: %[[POW2:.+]] = shl nuw i32 1, %[[SHIFT_AMOUNT]]
+    // CHECK: ret i32 %[[POW2]]
+    2u32.pow(exp)
+}
+
+// 4 ** n == 2 ** (2 * n) == 1 << (2 * n)
+// CHECK-LABEL: @pow4
+#[no_mangle]
+pub fn pow4(exp: u32) -> u32 {
+    // CHECK: %[[EXP2:.+]] = shl i32 %exp, 1
+    // CHECK: %[[SHIFT_AMOUNT:.+]] = and i32 %[[EXP2]], 30
+    // CHECK: %[[POW4:.+]] = shl nuw nsw i32 1, %[[SHIFT_AMOUNT]]
+    // CHECK: ret i32 %[[POW4]]
+    4u32.pow(exp)
+}
+
+// 16 ** n == 2 ** (4 * n) == 1 << (4 * n)
+// CHECK-LABEL: @pow16
+#[no_mangle]
+pub fn pow16(exp: u32) -> u32 {
+    // CHECK: %[[EXP2:.+]] = shl i32 %exp, 2
+    // CHECK: %[[SHIFT_AMOUNT:.+]] = and i32 %[[EXP2]], 28
+    // CHECK: %[[POW16:.+]] = shl nuw nsw i32 1, %[[SHIFT_AMOUNT]]
+    // CHECK: ret i32 %[[POW16]]
+    16u32.pow(exp)
+}