# How do you solve the exponential equation 5^(3x)=25^(x-4)?

Aug 24, 2017

$x = - 8$

#### Explanation:

As a first approach to solving exponential equations, try to either:

• make the bases the same
• make the indices the same.

In this case, notice that $25$ is a power of $5 , \text{ } \textcolor{b l u e}{25 = {5}^{2}}$

${5}^{3 x} = {\textcolor{b l u e}{25}}^{x - 4}$

${5}^{3 x} = {\textcolor{b l u e}{\left({5}^{2}\right)}}^{x - 4} \text{ } \leftarrow$ multiply the indices

${\textcolor{red}{5}}^{3 x} = {\textcolor{red}{5}}^{2 x - 8} \text{ } \leftarrow$ the bases are the same

$\therefore 3 x = 2 x - 8 \text{ } \leftarrow$ the indices are equal

$3 x - 2 x = - 8$

$x = - 8$