Properties and Formulas of Logarithms

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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}\,


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