# Solve the equation. \log 4x-\log(12+x)=\log 2

Solve the equation.
$\mathrm{log}4x-\mathrm{log}\left(12+x\right)=\mathrm{log}2$
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Derrick

Now using the formula ${\mathrm{log}}_{a}b-{\mathrm{log}}_{a}c=\mathrm{log}\frac{b}{c}$, simplify
$\mathrm{log}4x-\mathrm{log}\left(12+x\right)=\mathrm{log}2$ and solve for x.
$\mathrm{log}4x-\mathrm{log}\left(12+x\right)=\mathrm{log}2$
$\mathrm{log}\frac{4x}{12+x}=\mathrm{log}2$
$\frac{4x}{12+x}=2$
$4x=2\left(12+x\right)$
$=24+2x$
$4x-2x=24$
$2x=24$
$x=12$