Answer
$\log_{5}\frac{x^{2}y^{4}}{z^{6}}$
Work Step by Step
$2( \log_{5}x+2\log_{5}y-3\log_{5}z)=2( \log_{5}x+\log_{5}y^2-\log_{5}z^3)=2\log_{5}\frac{xy^{2}}{z^{3}}=\log_{5}(\frac{xy^{2}}{z^{3}})^{2}=\log_{5}\frac{x^{2}y^{4}}{z^{6}}$
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