Logarithms

math.log(x) gives the natural (base e) logarithm of x.

math.log(math.e)  # 1.0
math.log(1)       # 0.0
math.log(100)     # 4.605170185988092

math.log can lose precision with numbers close to 1, due to the limitations of floating-point numbers. In order to accurately calculate logs close to 1, use math.log1p, which evaluates the natural logarithm of 1 plus the argument:

math.log(1 + 1e-20)  # 0.0
math.log1p(1e-20)    # 1e-20

math.log10 can be used for logs base 10:

math.log10(10)  # 1.0

When used with two arguments, math.log(x, base) gives the logarithm of x in the given base (i.e. log(x) / log(base).

math.log(100, 10) # 2.0
math.log(27, 3)   # 3.0
math.log(1, 10)   # 0.0