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Solve for $x.$$$5^{2-3 x}=9^{4 x-5}$$

$$1.04317$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

00:46

Solve for $x$.$$5^…

00:33

01:37

Solve each equation.$$…

01:30

01:20

Solve the equation.$$(…

01:08

Solve each equation for $x…

04:42

02:31

Solve: $9^{x-1}=3^{x^{2}-5…

01:25

Solve.

$$\frac…

01:15

Solve the equation for $x$…

01:21

So we're gonna use a few law of logs to be able to solve this. Definitely want your calculator handy. I just did the previous problem using natural logs. To me, that's when I'll use log. But it doesn't actually matter. You can use any base that you want. So since I can use any base, I'll just use a log based 10. So that's what you wanna do. You do that to both sides. Eso The reason why we do that is then we can move this exponents in front and change that to be a multiplication problem. So this export could be moved in front become a multiplication problem. Now, the other thing is, you want to make sure you distribute log of five thio each piece. So if you don't do that, you'll get the wrong answer. So log of five times to analog of five times negative three x a long time is equal to four x from log of nine. And the way I have based 10 on both sides. But that actually doesn't matter. Could be any base you want minus five log of nine. So now what you have to do is get your ex is on the same side. So what I would do leave this to log of five alone. I would add the five log of nine to the left side. You know, to eliminate that, I'll leave the four x log of nine on the right side and then add, because I wanna move that piece to the right side. What? And if you're confused, the whole point is Aiken, then greatest common factor. The X out in this problem. So what I'm looking at is X times the quantity of four. Log of nine, plus three. Log of five. I'm leaving that left side alone. By the way, I don't know how much work your teacher would let you not show, but now it's a multiplication problem that you could solve by division. So X is going to be equal to that piece. Um, a songs you divide like this. Okay. Aan den. From there, it's just a matter of plugging into your calculator. So go to your calculator and plug that in. Um, I'm tempted to just copy from the previous problem that I had because there's too log of, but anyway, go to your calculator type it in. Plus five. Log of nine over or log of nine less. Three. Log of five. There we go. I got about 1.43 Perfect. And I would stop right there because I, like toe around to three decimal places. But my calculator does go on further. 164978 But three decibels is usually good enough. Yeah.

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