Properties and Formulas of Logarithms

Name

Properties and Formulas of Logarithms
Properties and Formulas Comments and Examples
$f(x)=a^x,\quad a\gt0\text{ and }a\neq1$ $\text{Exponential Function}\,$
$f(x)=log_{a}x,\quad a\gt0\text{ and }a\neq1$ $\text{Logarithmic Function}\,$
$\log_{b}m=\frac{\log_{a}m}{\log_{a}b}$ $\text{The Change-of-Base-Formula}\,$
$\log_{a}x=y \longleftrightarrow x=a^y\,$ $\text{A Logarithm is an Exponent}\,$
$\log_{a}1=0\,$ $\text{Property}\,$
$\log_{a}a=1\,$ $\text{Property}\,$
$\log_{a}a^x=x\,$ $\text{Property}\,$
$a^{\log_{a}x}=x$ $\text{Property}\,$
$\log_{a} mn=\log_{a}m+\log_{a}n\,$ $\text{The Product Rule}\,$
$\log_{a} \frac {m}{n}=\log_{a}m-\log_{a}n\,$ $\text{The Quotient Rule}\,$
$\log_{a}m^p=p\log_{a}m\,$ $\text{The Power Rule}\,$
$\log_{a}m^\frac{1}{r}=\frac{1}{r}\log_{a}m\,$ $\text{The Root Rule}\,$
$\log_{a}m=\log_{a}n\longleftrightarrow m=n,\text{ for }a\gt0\text{ and }a\neq1\,$ $\text{Property of Logarithmic Equality}\,$

Usage

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