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GH
Numerade Educator

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Problem 8 Easy Difficulty

For the following exercises, use like bases to solve the exponential equation.
$$
625 \cdot 5^{3 x+3}=125
$$

Answer

$-\frac{4}{3}$

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Alayna H.

McMaster University

Caleb E.

Baylor University

Video Transcript

So this is our problem. And the first step is to change everything to base. I So the 625 in the lunch 25. So let's just start with 625 here. So the trick is to divide five out. Then you get 225 2 by five. Out again, you get 25 by five hour again and you get 45 So you know that this is five to the fourth throws. Five reacts plus three. And we already know this. Since it's been our little true diagram here, we know that's five to the third power. And since we're multiplying like bases, we can add the four in the three explosive three to get five to the three X Plus seven equals five to the three. And since these are the same base, we use the 1 to 1 property and set their powers. You call to each other. So three X plus seven equals three. No track seven from both sides. Three. X equals negative four and divide by three. When we get our answers, X equals negative for over three

Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Alayna H.

McMaster University

Caleb E.

Baylor University