Answer
$2log_5x+4log_5y+\frac{3}{5}log_5m+\frac{1}{5}log_5p$
Work Step by Step
$log_5(x^2y^4\sqrt[5] {m^3p})=log_5x^2+log_5y^4+log_5m^{3/5}+log_5p^{1/5}=2log_5x+4log_5y+\frac{3}{5}log_5m+\frac{1}{5}log_5p$
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