Answer
$x=-2$
Work Step by Step
We rewrite both sides, so that the base is $\frac{2}{5}$ on both sides.
$(\frac{5}{2})^x=\frac{4}{25}
\\(\frac{5}{2})^x=(\frac{2}{5})^2$
By the law of exponents: $\frac{5}{2}^x=\frac{2}{5}^{-x}$.
Thus,
$(\frac{2}{5})^{-x}=(\frac{2}{5})^2$
Then we set the exponents equal, because the two sides are equal only if the powers are equal too:
$-x=2$
$x=-2$
