Answer
$= \frac{1}{5}\log_7 3 + \frac{3}{5}\log_7 x + \frac{1}{5}\log_7 y$
Work Step by Step
$\log_7 (\sqrt[5] {3x^{3}y})$
$= \log_7 (3x^{3}y)^{\frac{1}{5}}$
$= \log_7 (3^{\frac{1}{5}}x^{3 \times \frac{1}{5} }y^{\frac{1}{5}})$
$= \log_7 (3^{\frac{1}{5}}x^{\frac{3}{5} }y^{\frac{1}{5}})$
$= \log_7 (3^{\frac{1}{5}}) + \log_7 x^{\frac{3}{5}} + \log_7 y^{\frac{1}{5}}$
$= \frac{1}{5}\log_7 3 + \frac{3}{5}\log_7 x + \frac{1}{5}\log_7 y$
