Answer
$x=\frac{2 b}{1-a} $
Work Step by Step
Given that $2^a=5$ and $2^b=7$, we have
$$
\begin{aligned}
0.4^x & =49 \\
\left(\frac{2}{5}\right)^x & =7^2 \\
\left(2 \cdot 5^{-1}\right)^x & =7^2 \\
\left(2\left(2^a\right)^{-1}\right)^x & =7^2 \\
\left(2\left(2^{-a}\right)\right)^x & =7^2 \\
\left(2^{-a+1}\right)^x & =\left(2^b\right)^2 \\
2^{(1-a) x} & =2^{2 b} \\
(1-a) x & =2 b \\
x & =\frac{2 b}{1-a} .
\end{aligned}
$$
so $x=\frac{2 b}{1-a} $
