\log_{\sqrt{x}}a^4 \log_{a^2}\frac{4}{2-ax} = \frac{1}{\log_{a^4} \sqrt{x}} \log_{a^2}\frac{4}{2-ax} = \frac{1}{\log_{a^2} \sqrt[4]{x}} \log_{a^2}\frac{4}{2-ax} = \frac{\log_{a^2} \sqrt[4]{x}}{\log_{a^2}\frac{4}{2-ax}} = \log_{\frac{4}{2-ax}} \sqrt[4]{x}