Python math module logarithm functions [duplicate]

Question

Possible Duplicate:
Inaccurate Logarithm in Python

Why are the math.log10(x) and math.log(x,10) results different?

In [1]: from math import *

In [2]: log10(1000)
Out[2]: 3.0

In [3]: log(1000,10)
Out[3]: 2.9999999999999996

Answer 1

It's a known bug : http://bugs.python.org/issue3724

Seems logX(y) is always more precise than the equivalent log(Y, X).

Answer 2

math.log10 and math.log(x, 10) are using different algorithm, and the former is usually more accurate. Actually, it's a known issue(Issue6765): math.log, log10 inconsistency.

One may think in this way: log10(x) has a fixed base, hence it can be computed directly by some mathematical approximation formula(e.g. Taylor series), while log(x, 10) comes from a more general formula with two variables, which may be indirectly calculated by log(x) / log(10)(at least the precision of log(10) will affect the precision of quotient). So it's natural that the former way is both faster and more accurate, and that is reasonable considering that it takes advantage of a pre-known logarithmic base(i.e. 10).