Answer
$x=\frac{-3}{b}$
Work Step by Step
Given that $2^a=5$ and $2^b=7$, we have
$$
\begin{aligned}
7^x & =\frac{1}{8} \\
\left(2^b\right)^x & =\frac{1}{2^3} \\
2^{b x} & =2^{-3} \\
b x & =-3 \\
x & =\frac{-3}{b} .
\end{aligned}
$$
so $x=\frac{-3}{b}$
