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Write the given expression as a sum of logarithms.$$\log _{3} \frac{2}{y}$$

$$\log _{3} 2-\log _{3} y$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

Write the given expression…

01:17

01:50

01:32

01:12

01:23

Use the properties of loga…

03:43

Write the expression as on…

00:19

Use the Laws of Logarithms…

00:29

00:54

Express as a single logari…

Write logarithmic expressi…

01:20

05:12

00:46

right. This problem is applying the law of logs. Um, uses a division X divided by y, uh, and that law of log says the base teams the same so long based B of X and, uh, log based beat of Why the denominator that's equal to subtraction. Now, sometimes I'll tell my students just lowering the problem this way that these two are equal x y to the negative first. And then, uh, you won't have to remember that subtraction because then you could say, Well, it's log basically of X plus log Based B Uh huh. Why? To the negative first. And then in another law of logs, you learn that that negative first power comes in front. So how do we use that loss to this problem? We'll just follows directly from that log base. Three of two over. Why is going to equal? I'll just change colors. The base of three stays the same. It's a minus. You can't really see it anymore, but minus log based three because I'd say the same of why There you go. I meant to circle in green. There we go. This is the correct answer

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