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Combine the given expression into a single logarithm.$$3 \ln x+2 \ln y$$

$$\ln x^{3} y^{2}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

McMaster University

Lectures

00:46

Write the given expression…

00:58

Express as a single logari…

01:11

01:23

Combine the given expressi…

01:21

00:35

Write the following expres…

01:37

Write the expression as th…

Okay. This problem needs to law of logs in order to solve. And it's very important the order that you do this in, um, because you don't e repeat, you do not want to combine the law of logs with the addition Yet until, uh, it's like natural log only not the times three in front eso let me get to the actual rules, is you. It's very important that you start with the numbers in front to rewrite them as exponents. So this two needs to be rewritten as y squared. So what that looks like is that we have natural log of X cubed plus natural log of why squared Which takes me back to this. Plus now I guess I'm talking about this Plus, which if you're adding to logs with the same base in each of these bases are implied to be e. Then you multiply your terms. Eso We're actually ready to just write the final answer? It's natural log of X cubed times. Why squared on? There's your final answer. You might want to put in parentheses, but you don't have to. So let me circle this move on

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