<s>[INST] How to solve $\log_{4}(\sqrt{x^{4/3}})+3\log_{x}(16x)=7?$ 
How to solve $\log_{4}(\sqrt{x^{4/3}})+3\log_{x}(16x)=7?$

I've tried everything from brute force to doing base change but nothing works. I was wondering what was the best way in solving this?
 [/INST] \begin{align}
\log_{4}(\sqrt{x^{4/3}})+3\log_{x}(16x)&=7\\
\left(\frac{1}{2}\right)\left(\frac{4}{3}\right)\log_{4}(x)+3\log_{x}(4^2)+3\log_{x}(x)&=7\\
\frac{2}{3}\log_{4}(x)+\frac{6}{\log_4x}+3&=7\\
(\log_4x)^2-6\log_4x+9&=0\\
\log_4x&=3\\
x&=64
\end{align}
</s>