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.$$$12^{4 x+3}=15^{7-2 x}$$

$$0.74901$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

McMaster University

Idaho State University

Lectures

03:58

Solve each equation.$$…

03:37

Solve.$4 x^{2 / 3}+16 …

01:49

Solve each equation. $…

01:09

Solve.$\frac{3}{4} x^{…

02:19

Solve the equation $3 x^{7…

01:01

Solve for $x.$$$4^{3}=…

02:05

02:10

0:00

Solve.$(12 x-3)^{\frac…

Alright, This is, Ah, small trick and solving these types of problems. So we have 12 to the four X plus three. The thunder is equal to 15 to the seven minus two X, and it's up to you. If you want to log both sides or natural log both sides. I usually just hit the log, but I know some teachers probably have a preference, and the whole point is then we can move these exponents in front Now. The other thing that I would mention is that you could distribute, Um, because it's the quantity of four X plus three that's being multiplied by log. So I'm going to write it all out. Log of 12, uh, times cause I like to go the calculated the end plus log of 12 times three. Just move. The three in front is equal to seven. Log of 15 and at minus. Ah, log of 15 times two x. So from here, what I can do is get my ex is on the same side, so I'm looking at log 12 times for X Okay. Plus, I'm adding log of 15 to the left side. Times two X is equal to seven log of 15. And again, you could do all this with natural log. Just all my logs would be, um, l lens. Instead, you have to use a calculator anyway. And the whole premise is, once you get your ex is on the same side, you can factor the X in front and then times the quantity by me and do two steps at once. Because because I like to um yeah, eso imagine for a second I factored these pieces in front these exes in front. So it's just times this quantity. Well, then I hope you agree that that's the same. So then to solve a multiplication problem, Aiken divided over. So I'm looking at four log of 12 on. I just moved that four in front. Same thing here. So I'm gonna move this to in front, and then I'm gonna go to a calculator and just type this in, okay? Eso make sure you type it incorrectly. If your calculator has a fraction key, makes it a lot easier if it does not just put parentheses all in the numerator and all in the denominator, you should get the right answer. And yeah, I'm just typing in I hit Enter and I get an answer of 0.749 for X as I check the answer key that that does match. So, uh, E guess if you want around it any further than that, you know, 01 or further, But I like three decimals. There we go.

View More Answers From This Book

Find Another Textbook

01:11

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

00:53

Determine $f^{\prime}(x)$.$$f(x)=\ln 3 x$$

02:07

03:04

The population of Hungary is decreasing by $0.5 \%$ each year. Its populatio…

01:17

Find $x$.$$\log _{1 / 4} x=3 / 2$$

03:05

Evaluate the integral by substitution$$\int \frac{3 x+2}{\sqrt{x-1}} d x…

01:24

Compute the value of the given logarithm.$$\log _{5} 20$$

01:50

Use -0.000121 as the decay constant for Carbon 14.If an ancient wooden a…

01:19

Write the given expression in exponential format. $$\log 1 / 100=-2$$

01:10

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