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

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

We have

$49^{x} = 7 \sqrt{7}$ $49^x=7sqrt7$

Knowing that $49 = 7^{2}$ $49=7^2$ and $\sqrt{7} = 7^{\frac{1}{2}}$ $sqrt7=7^(1/2)$ , we get

$7^{2 x} = 7 \cdot 7^{\frac{1}{2}}$ $7^(2x)=7*7^(1/2)$

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

$7^{2 x} = 7^{\frac{3}{2}}$ $7^color(red)(2x)=7^color(red)(3/2)$

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

$2 x = \frac{3}{2} \Rightarrow x = \frac{3}{4}$ $2x=3/2=>x=3/4$