Question

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

Answer 1

`x=3/4`

Explanation:

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`