Name

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

Usage