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Combine the given expression into a single logarithm.$$2 \log _{3} 4-\log _{3} 2$$

$$\log _{3} 8$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

00:43

Write each logarithmic exp…

02:49

Combine the given expressi…

02:33

00:51

Rewrite the expression as …

00:47

00:37

Simplify to a single logar…

02:42

Condense the expression to…

01:22

00:21

Rewrite each expression as…

01:30

00:52

So we're undoing the law of logs in this problem, and we're starting to log based three or four minus log based three of two. Now, it's very important that you undo the, uh I guess the coefficients in front, uh, and turn them into exponents. Eso What we're looking at that is that this is equal to log based three. Now. You don't need parentheses. It's implied, but it's four squared, minus log based three of two. Now, if I were doing this problem, I would square the number first. I don't know, just a habit of mine. So looking at log base, three of four squared four times for 16 minus log based, three of two. And now we can use the law of logs that when we are subtracting, uh, we divide these two numbers so subtraction tells us to divide, and then we can write it as a single log log base. Three of 16 divided by two. Well, hey, I know that 16 divided by two is eight to this answer would be a long based three of eight, and that's all we can do. Anything beyond that would need a calculator

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