# Expand using logarithmic properties. Where possible, evaluate logarithmic expressions.

Expand using logarithmic properties. Where possible, evaluate logarithmic expressions.
${\mathrm{log}}_{5}\left(\frac{{x}^{3}\sqrt{y}}{125}\right)$
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Step 1
On simplification, we get

$={\mathrm{log}}_{5}\left({x}^{3}\right)+{\mathrm{log}}_{5}\left({y}^{\frac{1}{2}}\right)-{\mathrm{log}}_{5}\left({5}^{3}\right)$

$=3{\mathrm{log}}_{5}\left(x\right)+\frac{1}{2}{\mathrm{log}}_{5}\left(y\right)-3$