# How do you solve 4*5^(x/2)=500?

Jun 17, 2016

The value of color(blue)(x = 6

#### Explanation:

$\textcolor{b l u e}{4} \cdot {5}^{\frac{x}{2}} = 500$

 5 ^(x/2) = 500 / color(blue)(4

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

$125$ can also be expressed as ${5}^{3}$, so the expression now becomes:

${5}^{\frac{x}{2}} = {5}^{3}$
Now as the bases are equal we can equate the powers and obtain the value of $x .$

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

color(blue)(x = 6