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

May 14, 2018

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

#### Explanation:

We have

${49}^{x} = 7 \sqrt{7}$

Knowing that $49 = {7}^{2}$ and $\sqrt{7} = {7}^{\frac{1}{2}}$, we get

${7}^{2 x} = 7 \cdot {7}^{\frac{1}{2}}$

Using the property that ${\alpha}^{a} \cdot {\alpha}^{b} = {\alpha}^{a + b}$:

${7}^{\textcolor{red}{2 x}} = {7}^{\textcolor{red}{\frac{3}{2}}}$

Since we have $7$ as the base of the exponential function on both sides, let us take the ${\log}_{7}$ of both:

$2 x = \frac{3}{2} \implies x = \frac{3}{4}$