Name

**Properties and Formulas of Logarithms**
Properties and Formulas	Comments and Examples
$f(x)=a^x,\quad a>0\text{ and }a\neq1$	$\text{Exponential Function}\,$
$f(x)=log_{a}x,\quad a>0\text{ and }a\neq1$	$\text{Logarithmic Function}\,$
$\log_{b}m=\frac{\log_{a}m}{\log_{a}b}$	$\text{The Change-of-Base-Formula}\,$
$\log_{a}x=y \longleftrightarrow x=a^y\,$	$\text{A Logarithm is an Exponent}\,$
$\log_{a}1=0\,$	$\text{Property}\,$
$\log_{a}a=1\,$	$\text{Property}\,$
$\log_{a}a^x=x\,$	$\text{Property}\,$
$a^{\log_{a}x}=x$	$\text{Property}\,$
$\log_{a} mn=\log_{a}m+\log_{a}n\,$	$\text{The Product Rule}\,$
$\log_{a} \frac {m}{n}=\log_{a}m-\log_{a}n\,$	$\text{The Quotient Rule}\,$
$\log_{a}m^p=p\log_{a}m\,$	$\text{The Power Rule}\,$
$\log_{a}m^\frac{1}{r}=\frac{1}{r}\log_{a}m\,$	$\text{The Root Rule}\,$
$\log_{a}m=\log_{a}n\longleftrightarrow m=n,\text{ for }a>0\text{ and }a\neq1\,$	$\text{Property of Logarithmic Equality}\,$