Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Solve for $x.$$$4^{x+2}=3^{2-x}$$

$$-0.231544$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:37

Solve: $x^{3}+x^{2}=4 x+4$…

02:05

Solve.$x^{4}+3=4 x^{2}…

01:01

Solve for $x.$$$4^{3}=…

01:07

Solve.$$x^{2}+4 x=3$$<…

01:02

Solve: $x^{2}-4 x=3$

01:04

Solve:$x^{2}+3 x=4$

All right, so this problem is gonna involve a lot of arithmetic. Definitely. Want a calculator handy? Um, and it's up to you if you like to use logs or natural logs. I think because I've been using logs, I might switch over the natural log to show it doesn't actually matter. Eso The first step is because you're exponents have your exes. In order to solve this, you want to log or natural log both sides, so I'm gonna natural log. And the reason why this works is because now we can move this exponents in front just, uh, and it turns into a multiplication problem. Now, what I like to do is distribute that natural log a four to both terms so natural for Times X and natural Lago. Four times two the same thing on this one. I'd have to times natural log of three and then minus x times natural log of three eso that's distributing. So now what I like to do is get my ex is on the same side, so I'm gonna add this X natural log of three to the left side. And at the same time, I'm going to subtract to natural log afford to the right because that's how we do our inverse operations. So I'm almost at the end because on the left side I have the greatest common factor I can factor out that X. It's a natural before, plus natural leg of three and the right side. I'm not gonna do anything with just gonna leave it. You could factor out if you want, but it's actually kind of a waste of time because it's a giant multiplication problem. To get this to the other side would be with Division eso. Now, you could just go to a calculator. Just make sure that you either type it into your calculator using parentheses or you use a fraction tool depending on what calculator you use. So I'm doing to natural leg of three minus two natural law before. By the way, you could also use logs everywhere that I have natural log. You can put just log natural log of three. So I type that in and I got an answer for X. I liked around it three decimal places, so I would write to point Sorry. 0.232 Don't forget about the negative. I think I forgot to say it, But if you round further than that, uh, would be negative. 0.23 15 43 56 Uh, 52 And then my calculator stops, but there you go.

View More Answers From This Book

Find Another Textbook

02:53

02:34

Find and classify, using the second partial derivative test, the critical po…

00:51

Determine the value of the logarithm without the use of a calculator.$$\…

02:08

Use logarithmic differentiation to find the derivative.$$y=x^{e^{x}}$$

01:58

Determine the derivative.$$f(x)=\frac{e^{x}+1}{x^{2}-1}$$

01:56

Determine the equation of the tangent line at the given $x$ -coordinate.…

01:18

Use the properties of logarithms to find the derivative. Hint: It might be e…

02:50

03:16

For how long must $\$ 2200$ be left on deposit at $9.65 \%$ compounded conti…

02:27