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Write the given expression as a sum of logarithms.$$\log \sqrt{x y^{3}}$$

$$^{1 / 2} \log x+3 / 2 \log y$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:10

Write the given expression…

01:15

05:12

Write the expression as on…

01:12

01:17

00:36

Use the Laws of Logarithms…

01:25

Write the given logarithm …

01:43

01:45

01:06

00:25

Write each expression as a…

01:26

02:30

eso We actually have a couple of options on solving this problem, but they're all related to the same two rules. So I would do some manipulation first to help. I think the way I'm going to do it is going to be helpful. S o, This is the same thing as X Y cute to the one half power. Um, Now, most students are familiar with that rule and are pretty familiar with the square root is to the one half power. And then they're also familiar that if you take something to the one half power you have Thio, I shouldn't use the word distribute, but, you know, take every piece, every base inside of it to the one half hour as you multiply your exponents. One times one half is one half and three times one half is three halfs. So now it makes more sense for students using the law of logs to recognize the multiplication, get split as an addition problem. And then from there, any exponents you get, you can move to the front. And this is your correct answer of one half log of X plus three halves. Log of why now, If anybody is curious. I mean, circle this because that's the answer. What you could have done as well is brought the one half of power in front first, um, and then from there, basically, what I'm doing is factoring out a one half in this answer. Um, and you can double check that. What I'm writing down is correct. And it iss sure.

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