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

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Answer 1 · 2018-05-14T18:21:03

$x=3/4$

We have

$49^x=7sqrt7$

Knowing that $49=7^2$ and $sqrt7=7^(1/2)$ , we get

$7^(2x)=7*7^(1/2)$

Using the property that $alpha^a*alpha^b=alpha^(a+b)$ :

$7^color(red)(2x)=7^color(red)(3/2)$

Since we have $7$ as the base of the exponential function on both sides, let us take the $log_7$ of both:

$2x=3/2=>x=3/4$