bLogarithms/b are the inverse of exponentials.

If (f(x) = a^x ), then (f^{-1}(x) = \log_a{x} ).

Alternatively:

(a^x = y \iff x = \log_a{y} )

where (a > 0), (a \neq 1) and (x ≥ 0).

(\log_a{y}) is pronounced "(\log) base (a) of (y)".

Where the base is omitted, i.e. (\log{y}), the base is assumed to be (10).

[b]uNatural logarithms[/u]/b

When the base is the natural base (e), i.e. (\log_e), there is a special notation: (\ln).

Accordingly, if (f(x) = e^x ), then (f^{-1}(x) = \ln{x} ).

Alternatively:

(e^x = y \iff x = \ln{y} )

[b]uGraph of the natural logarithm[/u]/b

(y=\ln{x} \quad \textcolor{blue}{y=e^x} )

mtaimg/images/topics/6/6-64-1.png/mtaimg

[b]uLogarithms[/u]/b

(a^x = y \iff x = \log_a{y} )

(e^x = y \iff x = \ln{y} )