# How do you solve (log_x (7)(log_7 (5)) = 6?

$\frac{\log 7}{\log x} \cdot \frac{\log 5}{\log 7} = 6 \to \log \frac{5}{\log} x = 6 \to {\log}_{x} 5 = 6 \to {x}^{6} = 5 \to x = {5}^{\frac{1}{6}} = \sqrt[6]{5}$
Use change of base formula${\log}_{b} x = \log \frac{b}{\log} x$ to rewrite each logarithm and then simplify then solve for x