# How do you solve \sqrt { 125} = 5^ { x }?

Jun 30, 2018

$x = \frac{3}{2}$

#### Explanation:

$\sqrt{125} = {125}^{\frac{1}{2}}$

$125 = {5}^{3}$

$\implies {125}^{\frac{1}{2}} = {\left({5}^{3}\right)}^{\frac{1}{2}}$

$\implies {5}^{x} = {\left({5}^{3}\right)}^{\frac{1}{2}}$

$\implies {5}^{x} = {5}^{\frac{3}{2}}$

Considering the exponents:

$x = \frac{3}{2}$

Jun 30, 2018

$x = \frac{3}{2}$

#### Explanation:

We can rewrite $\sqrt{125}$ as ${125}^{\frac{1}{2}}$. This now gives us

${125}^{\frac{1}{2}} = {5}^{x}$

Let's make our bases the same. $125 = {5}^{3}$, so we can rewrite the equation as

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

Since our bases are the same, the exponents are equal.

${5}^{\frac{3}{2}} = {5}^{x}$

$\implies \frac{3}{2} = x$

$x = \frac{3}{2}$

Hope this helps!