diff --git a/src/libcore/num/mod.rs b/src/libcore/num/mod.rs
index f4a1afd436adb..c073a6ca04e47 100644
--- a/src/libcore/num/mod.rs
+++ b/src/libcore/num/mod.rs
@@ -2160,6 +2160,115 @@ assert_eq!((-a).rem_euclid(-b), 1);
             }
         }
 
+        doc_comment! {
+            concat!("Returns the logarithm of the number with respect to an arbitrary base.
+
+Returns `None` if the number is negative or zero, or if the base is not at least 2.
+
+This method may not be optimized owing to implementation details;
+`self.checked_log2()` can produce results more efficiently for base 2, and
+`self.checked_log10()` can produce results more efficiently for base 10.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let five = 5", stringify!($SelfT), ";
+
+// log5(5) == 1
+let result = five.checked_log(5);
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log(self, base: Self) -> Option<Self> {
+                // SAFETY: We check the input to this is always positive
+                let logb2 = |x: Self| unsafe { intrinsics::ctlz_nonzero(1 as Self) - intrinsics::ctlz_nonzero(x) };
+
+                if self <= 0 || base <= 1 {
+                    None
+                } else {
+                    let mut n = 0;
+                    let mut r = self;
+
+                    // Optimization for 128 bit wide integers.
+                    if mem::size_of::<Self>() * 8 == 128 {
+                        let b = logb2(self) / (logb2(base) + 1);
+                        n += b;
+                        r /= base.pow(b as u32);
+                    }
+
+                    while r >= base {
+                        r /= base;
+                        n += 1;
+                    }
+                    Some(n)
+                }
+            }
+        }
+
+        doc_comment! {
+            concat!("Returns the base 2 logarithm of the number.
+
+Returns `None` if the number is negative or zero.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let two = 2", stringify!($SelfT), ";
+
+// checked_log2(2) == 1
+let result = two.checked_log2();
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log2(self) -> Option<Self> {
+                if self <= 0 {
+                    None
+                } else {
+                    // SAFETY: We just checked that this number is positive
+                    let log = unsafe { intrinsics::ctlz_nonzero(1 as Self) - intrinsics::ctlz_nonzero(self) };
+                    Some(log)
+                }
+            }
+        }
+
+        doc_comment! {
+            concat!("Returns the base 10 logarithm of the number.
+
+Returns `None` if the number is negative or zero.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let ten = 10", stringify!($SelfT), ";
+
+// checked_log10(10) == 1
+let result = ten.checked_log10();
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log10(self) -> Option<Self> {
+                self.checked_log(10)
+            }
+        }
+
         doc_comment! {
             concat!("Computes the absolute value of `self`.
 
@@ -4169,6 +4278,115 @@ assert_eq!(7", stringify!($SelfT), ".rem_euclid(4), 3); // or any other integer
             }
         }
 
+        doc_comment! {
+            concat!("Returns the logarithm of the number with respect to an arbitrary base.
+
+Returns `None` if the number is zero, or if the base is not at least 2.
+
+This method may not be optimized owing to implementation details;
+`self.checked_log2()` can produce results more efficiently for base 2, and
+`self.checked_log10()` can produce results more efficiently for base 10.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let five = 5", stringify!($SelfT), ";
+
+// log5(5) == 1
+let result = five.checked_log(5);
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log(self, base: Self) -> Option<Self> {
+                // SAFETY: We check the input to this is always positive.
+                let logb2 = |x: Self| unsafe { intrinsics::ctlz_nonzero(1 as Self) - intrinsics::ctlz_nonzero(x) };
+
+                if self <= 0 || base <= 1 {
+                    None
+                } else {
+                    let mut n = 0;
+                    let mut r = self;
+
+                    // Optimization for 128 bit wide integers.
+                    if mem::size_of::<Self>() * 8 == 128 {
+                        let b = logb2(self) / (logb2(base) + 1);
+                        n += b;
+                        r /= base.pow(b as u32);
+                    }
+
+                    while r >= base {
+                        r /= base;
+                        n += 1;
+                    }
+                    Some(n)
+                }
+            }
+        }
+
+        doc_comment! {
+            concat!("Returns the base 2 logarithm of the number.
+
+Returns `None` if the number is zero.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let two = 2", stringify!($SelfT), ";
+
+// checked_log2(2) == 1
+let result = two.checked_log2();
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log2(self) -> Option<Self> {
+                if self <= 0 {
+                    None
+                } else {
+                    // SAFETY: We just checked that this number is positive
+                    let log = unsafe { intrinsics::ctlz_nonzero(1 as Self) - intrinsics::ctlz_nonzero(self) };
+                    Some(log)
+                }
+            }
+        }
+
+        doc_comment! {
+            concat!("Returns the base 10 logarithm of the number.
+
+Returns `None` if the number is zero.
+
+# Examples
+
+```
+#![feature(int_log)]
+
+let ten = 10", stringify!($SelfT), ";
+
+// checked_log10(10) == 1
+let result = ten.checked_log10();
+
+assert_eq!(result, Some(1));
+```"),
+            #[unstable(feature = "int_log", issue = "70887")]
+            #[must_use = "this returns the result of the operation, \
+                          without modifying the original"]
+            #[inline]
+            pub fn checked_log10(self) -> Option<Self> {
+                self.checked_log(10)
+            }
+        }
+
         doc_comment! {
             concat!("Returns `true` if and only if `self == 2^k` for some `k`.
 
diff --git a/src/libcore/tests/lib.rs b/src/libcore/tests/lib.rs
index 68a5e20a66fdc..16eaabf1e1fa8 100644
--- a/src/libcore/tests/lib.rs
+++ b/src/libcore/tests/lib.rs
@@ -13,6 +13,7 @@
 #![feature(fmt_internals)]
 #![feature(hashmap_internals)]
 #![feature(try_find)]
+#![feature(int_log)]
 #![feature(is_sorted)]
 #![feature(pattern)]
 #![feature(range_is_empty)]
diff --git a/src/libcore/tests/num/int_log.rs b/src/libcore/tests/num/int_log.rs
new file mode 100644
index 0000000000000..12557641d8a20
--- /dev/null
+++ b/src/libcore/tests/num/int_log.rs
@@ -0,0 +1,64 @@
+#[test]
+fn checked_log() {
+    assert_eq!(999u32.checked_log(10), Some(2));
+    assert_eq!(1000u32.checked_log(10), Some(3));
+    assert_eq!(555u32.checked_log(13), Some(2));
+    assert_eq!(63u32.checked_log(4), Some(2));
+    assert_eq!(64u32.checked_log(4), Some(3));
+    assert_eq!(10460353203u64.checked_log(3), Some(21));
+    assert_eq!(10460353202u64.checked_log(3), Some(20));
+    assert_eq!(147808829414345923316083210206383297601u128.checked_log(3), Some(80));
+    assert_eq!(147808829414345923316083210206383297600u128.checked_log(3), Some(79));
+    assert_eq!(22528399544939174411840147874772641u128.checked_log(19683), Some(8));
+    assert_eq!(22528399544939174411840147874772631i128.checked_log(19683), Some(7));
+
+    for i in i16::MIN..=0 {
+        assert_eq!(i.checked_log(4), None);
+    }
+    for i in 1..=i16::MAX {
+        assert_eq!(i.checked_log(13), Some((i as f32).log(13.0) as i16));
+    }
+    for i in 1..=u16::MAX {
+        assert_eq!(i.checked_log(13), Some((i as f32).log(13.0) as u16));
+    }
+}
+
+#[test]
+fn checked_log2() {
+    assert_eq!(5u32.checked_log2(), Some(2));
+    assert_eq!(0u64.checked_log2(), None);
+    assert_eq!(128i32.checked_log2(), Some(7));
+    assert_eq!((-55i16).checked_log2(), None);
+
+    for i in 1..=u8::MAX {
+        assert_eq!(i.checked_log2(), Some((i as f32).log2() as u8));
+    }
+    for i in 1..=u16::MAX {
+        assert_eq!(i.checked_log2(), Some((i as f32).log2() as u16));
+    }
+    for i in i8::MIN..=0 {
+        assert_eq!(i.checked_log2(), None);
+    }
+    for i in 1..=i8::MAX {
+        assert_eq!(i.checked_log2(), Some((i as f32).log2() as i8));
+    }
+    for i in i16::MIN..=0 {
+        assert_eq!(i.checked_log2(), None);
+    }
+    for i in 1..=i16::MAX {
+        assert_eq!(i.checked_log2(), Some((i as f32).log2() as i16));
+    }
+}
+
+#[test]
+fn checked_log10() {
+    for i in i16::MIN..=0 {
+        assert_eq!(i.checked_log10(), None);
+    }
+    for i in 1..=i16::MAX {
+        assert_eq!(i.checked_log10(), Some((i as f32).log10() as i16));
+    }
+    for i in 1..=u16::MAX {
+        assert_eq!(i.checked_log10(), Some((i as f32).log10() as u16));
+    }
+}
diff --git a/src/libcore/tests/num/mod.rs b/src/libcore/tests/num/mod.rs
index 939f1325c8499..51f67c363f84a 100644
--- a/src/libcore/tests/num/mod.rs
+++ b/src/libcore/tests/num/mod.rs
@@ -26,6 +26,7 @@ mod u8;
 mod bignum;
 mod dec2flt;
 mod flt2dec;
+mod int_log;
 
 /// Adds the attribute to all items in the block.
 macro_rules! cfg_block {