diff --git a/Lib/random.py b/Lib/random.py
index ef0034adce5..76627309e28 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -50,7 +50,7 @@ from warnings import warn as _warn
 from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
 from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
 from math import tau as TWOPI, floor as _floor, isfinite as _isfinite
-from math import lgamma as _lgamma, fabs as _fabs
+from math import lgamma as _lgamma, fabs as _fabs, log2 as _log2
 from os import urandom as _urandom
 from _collections_abc import Sequence as _Sequence
 from operator import index as _index
@@ -764,11 +764,11 @@ class Random(_random.Random):
             # BG: Geometric method by Devroye with running time of O(np).
             # https://dl.acm.org/doi/pdf/10.1145/42372.42381
             x = y = 0
-            c = _log(1.0 - p)
+            c = _log2(1.0 - p)
             if not c:
                 return x
             while True:
-                y += _floor(_log(random()) / c) + 1
+                y += _floor(_log2(random()) / c) + 1
                 if y > n:
                     return x
                 x += 1