Logarithm

Keywords: logarithm

The base a logarithm of number b is the power to which number a must be raised in order to get number b

${a}^{lo{g}_{a}b}=b$

Important logarithm identities

$lo{g}_{a}a=1$
$lo{g}_{a}1=0$
$lo{g}_{a}{a}^{n}=n$

Logarithmic identities

$lo{g}_{a}\left(xy\right)=lo{g}_{a}x+lo{g}_{a}y$
$lo{g}_{a}\left(\frac{x}{y}\right)=lo{g}_{a}x-lo{g}_{a}y$
$lo{g}_{a}{x}^{n}=nlo{g}_{a}x$

Changing the base of a logarithm

$lo{g}_{a}x=\frac{lo{g}_{b}x}{lo{g}_{b}a}$
$lo{g}_{a}b·lo{g}_{b}a=1$
${a}^{lo{g}_{b}c}={c}^{lo{g}_{b}a}$
$lo{g}_{a}x=lo{g}_{{a}^{n}}{x}^{n}$