Answer
$x=3$
Work Step by Step
We are given that $25^{x}=125^{x-1}$. Both of these numbers are powers of 5, so we can rewrite the equation as $(5^{2})^{x}=(5^{3})^{x-1}$.
This can be rewritten as $5^{2x}=5^{3x-3}$
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $2x=3x-3$. To solve for x, subtract 3x from both sides.
$-x=-3$
Divide both sides by -1.
$x=3$
