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Write the given expression as a sum of logarithms.$$\log 10 x^{2} y^{3}$$

$$1+2 \log x+3 \log y$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

McMaster University

University of Michigan - Ann Arbor

Lectures

00:38

Write the expression as a …

01:25

Write the given expression…

01:17

01:43

00:26

Rewrite the equation using…

00:29

Use the Laws of Logarithms…

00:21

0:00

Use the laws of logarithms…

01:50

01:12

00:20

right. So in this problem, we're going to simplify Log base. 10. I'll go ahead and write the 10 in there, even though it's not written on the problem. Uh, it's implied. Just like the square root is implied to be a two, as the index on the main thing in this problem I'm not gonna write out the rules now is when you see multiplication, you can split up those logs, then with an addition problem. So Log based, 10 of 10 plus Log based 10 of X Squared plus Log based 10 of y Cube. But we're not done in. The reason why we're not done is there's a couple things that weaken Dio. First of all, the premise of Log based 10 of 10. Well, what this means is tend to some power is equal to 10. Um, now some people just memorized if the base and this number of the same that it's equal toe one but should make sense because tend to the first power will give you 10. So it is one there. The second thing is, the law of log says we can move it to in front. So this is to log based 10 of X and in the same manner. We could move this three in front. We're looking at three Log based, 10 of why, and by the way, you do not have to write this 10 here. It's implied, as I said at the beginning, So here's your answer.

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