<s>[INST] Solve the equation $4^{7 x - 10} = 10^{7 x - 6}$ for $x$ Solve for $x$ of the following equation. 
$$4^{7 x - 10} = 10^{7 x - 6}$$
I tried to make $4$ and $10$ have a common base but I could not find one so I don't know where to go from here. 
 [/INST] $$
\begin{align}
& 4^{7 x - 10} = 10^{7 x - 6} \\[6pt]
\implies & \log_4(4^{7 x - 10}) = \log_4(10^{7 x - 6}) \\[6pt]
\implies & 7x-10 = (7x-6)\log_4(10) \\[6pt]
\implies & 7x-7x\log_4(10) = 10-6\log_4(10) \\[6pt]
\implies & 7x[1-\log_4(10)] = 10-6\log_4(10) \\[6pt]
\implies & 7x = \frac{10-6\log_4(10)}{1-\log_4(10)} \\[6pt]
\implies & x = \frac{10-6\log_4(10)}{7-7\log_4(10)}
\end{align}
$$
</s>