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. 

$$4^{7x - 10} = 10^{7x - 6}$$
$$(7x - 10)\log4 = (7x - 6)\log10$$
$$7x = \frac{6\log10 - 10\log4}{\log10 - \log4}$$
$$ = \frac{6\log5 + 6\log2 - 20\log2}{\log5 + \log2 - 2\log2}$$
$$ = \frac{6\log5 - 14\log2}{\log5 - \log2}$$
$$ x = \frac{2(3\log5 - 7\log2)}{7(\log5 - \log2)}$$
