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GH
Numerade Educator

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Problem 6 Easy Difficulty

For the following exercises, use like bases to solve the exponential equation.
$$
3^{2 x+1} \cdot 3^{x}=243
$$

Answer

$\frac{4}{3}$

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Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Video Transcript

So the question is three to the two of us possible I'm times through to the X is equal to 243. So if Rex so the first step is to convert 243 to base through. So I do. This is make like a simple tree diagram. So divide three out. You get 81 right through it again. You're 27 by three. Out. Get nine. Divide the last three out and you get three. So how many threes you have? 12 or 345 threes. So you know that 243 is three to the fifth power? No. On the left side, since we're multiplying like bases re add their powers. So three to the two x plus one plus x Simplify that three to the three x plus one equals through to the fifth. Now, according to the one to the 1 to 1 property, we set their powers equal to each other. So three x plus one close by. Subtract one from both sides. Three X equals four and divide by three and we find the X equals for over three

Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University