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

$$\log _{2} x+2 \log _{2} y$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:17

Write the given expression…

01:15

00:51

Write logarithmic expressi…

01:25

00:57

Write the expression using…

Expand the logarithms as s…

00:35

Write each sum as a single…

03:43

Write the expression as on…

01:28

Condense the expression to…

00:29

Write logarithm as the sum…

00:14

Write each logarithm as a …

Write the expression as th…

03:48

Express as a sum or a diff…

all right on this problem. We're looking at log. We're actually doing to rules. Um, log base B. I hesitant to use. Ah, I'll use em in N eso. The first rule that we're gonna do is when you're multiplying inside of a base, you can split it up with addition broad based B of n and the second rule that we have is long base b of just picking out other letters of P to the Q power eyes equal to move in that queue in front. Wow, Oops. Forgot to write out the queue in front long base B of P. Times Q. Eso Now we can establish the answer that we need. And maybe you don't even need that second law because I can really explain this A second way log based two of X y squared because it makes sense then to say, Okay, well, that's, uh, log base to of X times y times. Why? Well, there's two multiplication is in there, so you could say Okay, well, that's long based. Two of X plus log based two of why, plus long based two of why? Well, how many log based two of wise do I have. There's two of them. So what's my final answer? Can't really do anything with that long based two of X, but we have to log based two of why Andre is your final answer.

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