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Solve for $x$ in.$$9^{3 x+2}=27^{2+x}$$

$$2 / 3$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

03:02

Solve the equation.$$9…

02:01

Solve for x: 3^x = 9^x-2

02:10

01:21

Solve for $x$ in.$$\fr…

01:31

Solve the equation.$$2…

00:59

02:22

Solve for $x$.$$9^…

01:40

Solve the equation for $x$…

01:02

Solve each equation.$$…

01:54

Solve the equation.$27…

05:25

Solve $x^{3}-9 x=2 x^{2}-1…

So if we want to solve this, the first thing we should do is try to get a common based on either side. So on the left side notice that we can rewrite nine as three squared and we can write 27 as three cute and then we'll just go ahead and leave everything else the same on both sides. Now remember, when we have a power to power, we can multiply the power together. So this would be three race of the two times three X plus two and then on the right side, this would be three raise the three times two X plus two or two plus X. I think I said something different. But now that we have the same basis here, we can go ahead and set the powers equal to each other. And I'll go ahead and distribute the two and three all of that. So this would be six X plus four is going to be too six plus three acts and then let me make sure I just multiply that rate. Yeah, and now we can just go ahead and solve for X. So I'm first going to subtract three x over, so that gives us three X on the left. I'm going to subtract four. That gives us two. Then we can go ahead and divide three. So that gives us X is equal to two thirds, so that will end up being our solution.

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