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

$$1 / 2 \ln x+2 \ln y$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:17

Write the given expression…

01:43

01:50

01:10

03:48

Express as a sum or a diff…

00:29

Write the expression as th…

00:41

Rewrite the expression in …

00:34

Express as a sum of logari…

00:25

Use the Laws of Logarithms…

All right. So this problem is all about knowing and, uh, law of logs because there's a multiplication in here and we're going to do some manipulation with exponents. Eso The first law of logs I'm going to use is when you're multiplying, you can split up the exponents. We're sorry, the these places, um, with addition, that is a law of law. Now, the other manipulation that I would say, is that you should understand that X the square root of X is the same thing is to the one half power. And that will make our second step even easier if you don't believe me, can plug into a calculator and see like the square root of nine equals three will nine to the one half power also equals three works for all numbers. Is taking that exponents? Here's the second law of logs, by the way, or moving that exponents in front that term and it turns into a multiplication. So we're ready for a final answer. Already won half natural aga Becks plus two natural log of y and there is your answer

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