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Solve for $x.$$$3^{x}=32$$

$$3.15465$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Lectures

00:51

Solve for $x$.$$3^{x}=…

01:17

Solve for $x.$$$3^{x}=…

00:39

Solve for $x$ algebraicall…

00:54

01:09

Solve.$$3^{x}=27

02:15

Solve.$$x^{2 / 3}=x$$<…

01:01

02:52

Solve $x^{2}=3-x$.

uh, s So we have this problem of three to the X is equal to 32 and we are going to use the law of logs to solve this. What I typically ask my students first is what answer makes sense. Because if you start going through, what is it? Three to the first? Okay, well, no, that would give me three is a three squared. Well, that gives me nine. Or still not good enough. Three to the third. Three times. Three times three has 27. So we're getting close. If we did three to the fourth, it'll be 81. So my students at least I asked them to say, Well, what's about X? Gonna be first and they should be able to say, Well, it's three point something. Well, let me show you how you can actually get this answer, and you do it by taking the log or natural log of both sides. Most of my students have used log. Um, I don't really know why they have a preference to that, but the reason why you want to take the same thing on both sides same log is now. You can move that exponents in front eso we're looking at X Times log of three is equal to log of 32 now no teachers going to expect you to know what that answer is. Um, they expect you to use a calculator because now you have a multiplication problem that you can solve by division. You can divide log of three over so these pieces will cancel. And now, as I go to my calculator and type that in log of 32 divided by log of three, I get about 3.15464876 something eso I liked around the three decimals, so I would write 30.155 But again, the answer was 3.154648768

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