Mathematics

Algebra

(reference 2.1)

Exponents	Logarithms
$a^x a^y = a^{x+y}$	$\log_b{b} = 1$
$\left( ab \right) ^x = a^x b^x$	$\log_b{1} = 0$
$\left( a^x \right) y = a^xy$	$\log_b \left( MN \right) = log_b{M} + log_b{N}$
$a^{mn} = \left( a^m \right) ^n$	$\log_b \left( \frac{M}{N} \right) = \log_b{M} - \log_b{N}$
$a^0 = 1$ If (a \neq 0)	$\log_b \left( M^p \right) = p \log_b{M}$
$a^{-x} = \frac{1}{a^x}$	$\log_b \left( \frac{1}{M} \right) = -\log_b{M}$
$\frac{a^x}{a^y} = a^{x-y}$	$\log_b{\sqrt[q]{M}} = \frac{1}{q} \log_b{M}$
$\sqrt[x]{ab} = \left( \sqrt[x]{a} \right) \left( \sqrt[x]{b} \right)$	$\log_b{M} = \left(\log_c{M} \right) \left(\log_b{c} \right)= \frac{\log_c{M}}{\log_c{b}}$
$a^{\frac{x}{y}} = \sqrt[y]{a^x} = \left( \sqrt[y]{a} \right)^x$
$a^{\frac{1}{y}} = \sqrt[y]{a}$
$\left( \sqrt[x]{a} \right) \left( \sqrt[y]{a} \right) = a^{\left( \frac{1}{x} + \frac{1}{y} \right)} = \sqrt[xy]{a^{x+y}}$
$\sqrt{a} + \sqrt{b} = \sqrt{a + b + 2\sqrt{ab}}$