Nasty.  Here is the test extracted from test/test_cmath.py

import math, cmath

test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
positive = test_values + [1.] + [1./x for x in test_values]
for base in [0.5, 2., 10.]:
    for v in positive:
        z = cmath.log(v, base)
        x = math.log(v,base)
        print(base, v, z, x, z.real-x)

On Winxp 3.0b1, |difference| is usually 0.0, else < 2.8e-17
6.6438561897747244 is, for instance, log2(100).
It is also the first pair tested: log(.01, base=.5)
0.7124414133982310 is not close to any valid test output.

On your system, is cmath64.log totally broken or just for base < 1?