# Simplify (condense) the following expression.7log5p−log5q7log5⁡p−log5⁡q&nbsp;&nbsp;

Simplify (condense) the following expression.

$7{\mathrm{log}}_{5}p-{\mathrm{log}}_{5}q$

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$7{\mathrm{log}}_{5}\left(p\right)-{\mathrm{log}}_{5}\left(q\right)$

Simplify $7{\mathrm{log}}_{5}\left(p\right)$ by moving $7$ inside the logarithm.

${\mathrm{log}}_{5}\left({p}^{7}\right)-{\mathrm{log}}_{5}\left(q\right)$

Use the quotient property of logarithms, ${\mathrm{log}}_{b}\left(x\right)-{\mathrm{log}}_{b}\left(y\right)={\mathrm{log}}_{b}\left(\frac{x}{y}\right)$.

${\mathrm{log}}_{5}\left(\frac{{p}^{7}}{q}\right)$