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Applying Properties of Logarithms

Applying Properties of Logarithms

Author: Anthony Varela
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Applying Properties of Logarithms

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Tutorial
Formulas to Know
Change of Base Property of Logs

log subscript b left parenthesis x right parenthesis equals fraction numerator log subscript a left parenthesis x right parenthesis over denominator log subscript a left parenthesis b right parenthesis end fraction

Logarithmic Form to Exponential Form

log subscript b open parentheses y close parentheses equals x space left right arrow y equals b to the power of x

Other Properties of Logs

log subscript b left parenthesis b right parenthesis equals 1

log subscript b left parenthesis 1 right parenthesis equals 0

Power Property of Logs

log subscript b open parentheses x to the power of n close parentheses equals n times log subscript b left parenthesis x right parenthesis

Product Property of Logs

log subscript b left parenthesis x y right parenthesis equals log subscript b left parenthesis x right parenthesis plus log subscript b left parenthesis y right parenthesis

Quotient Property of Logs

log subscript b open parentheses x over y close parentheses equals log subscript b left parenthesis x right parenthesis minus log subscript b left parenthesis y right parenthesis