Logarithms

This table describes how to type logarithmic expressions, along with usage examples (including the typeset equivalent.) If the expression you need is not listed, please define your own and explain the meaning of your notation.

Expression Description Examples

$\displaystyle \ln{x}$

The natural logarithm, base , of .

$\displaystyle \ln{x}=y \Longleftrightarrow e^y=x$

ln(x) = y <==> e^y = x

$\displaystyle \log{x}$

The common logarithm, base 10, of .

$\displaystyle \log{x}=y \Longleftrightarrow 10^y=x$

log(x) = y <==> 10^y = x

$\displaystyle \log_b{x}$

The logarithm, base , of .

$\displaystyle \mathrm{log_{b}}x=y \Longleftrightarrow \mathrm{b}^y=x$

log_b(x) = y <==> b^y = x

Expression	Description	Examples
$\displaystyle \ln{x}$	The natural logarithm, base , of .	$\displaystyle \ln{x}=y \Longleftrightarrow e^y=x$ ln(x) = y <==> e^y = x
$\displaystyle \log{x}$	The common logarithm, base 10, of .	$\displaystyle \log{x}=y \Longleftrightarrow 10^y=x$ log(x) = y <==> 10^y = x
$\displaystyle \log_b{x}$	The logarithm, base , of .	$\displaystyle \mathrm{log_{b}}x=y \Longleftrightarrow \mathrm{b}^y=x$ log_b(x) = y <==> b^y = x