Logarithmic equation for y

Given: $\log_4 5 = (\log_4 y)(\log_6 5^{1/2})$ $\log_4 5 = (\log_4 y) \cdot \frac{1}{2} \log_6 5$

Divide both sides by $\log_4 5$: $1 = \frac{\log_4 y}{\log_4 5} \cdot \frac{1}{2} \log_6 5$ $1 = \log_5 y \cdot \frac{1}{2 \log_5 6}$ $2 \log_5 6 = \log_5 y$ $\log_5 6^2 = \log_5 y \implies y = 36$