# Hello friends, please, I need to know how to get the answer out of this exponential equation?

Nov 3, 2016

$x = \frac{3}{4}$

#### Explanation:

Recall that $\sqrt{x} = {x}^{\frac{1}{2}} , \mathmr{and} {x}^{a} \cdot {x}^{b} = {x}^{a + b}$,

${5}^{2 x + 1} = 25 \sqrt{5}$
$\implies {5}^{2 x + 1} = {5}^{2} \cdot {5}^{\frac{1}{2}} = {5}^{2 + \frac{1}{2}} = {5}^{\frac{5}{2}}$
$\implies 2 x + 1 = \frac{5}{2}$
$\implies 2 x = \frac{5}{2} - 1 = \frac{3}{2}$
$x = \frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$