Answer
$x=\frac{4}{b+1}$
Work Step by Step
Given that $2^a=5$ and $2^b=7$, we have
$$
\begin{aligned}
14^x & =16 \\
(2 \cdot 7)^x & =16 \\
\left(2 \cdot 2^b\right)^x & =16 \\
\left(2^{b+1}\right)^x & =16 \\
2^{(b+1) x} & =2^4 \\
(b+1) x & =4 \\
x & =\frac{4}{b+1} .
\end{aligned}
$$
so $x=\frac{4}{b+1}$
