#### Answer

$x=3$

#### Work Step by Step

$25^{x}=125^{x-1}$
Rewrite $25$ as $5^{2}$ and $125$ as $5^{3}$:
$(5^{2})^{x}=(5^{3})^{x-1}$
Multiply the exponents on both sides of the equation:
$5^{2x}=5^{3x-3}$
If $5^{2x}=5^{3x-3}$, then $2x=3x-3$:
$2x=3x-3$
Solve for $x$:
$2x-3x=-3$
$-x=-3$
$x=3$