# How do you solve 25^(x-1)=125^(4x)?

Aug 19, 2016

$x = - \frac{1}{5}$

#### Explanation:

Since $25 = {5}^{2}$ and $125 = {5}^{3}$ you can rewrite:

${5}^{2 \left(x - 1\right)} = {5}^{3 \left(4 x\right)}$

that implies:

$2 \left(x - 1\right) = 3 \left(4 x\right)$

that's

$2 x - 2 = 12 x$

$10 x = - 2$

$x = - \frac{1}{5}$