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Write the given expression as a sum of logarithms.$$\ln \frac{x^{3} y^{4}}{z^{5}}$$

$$3 \ln x+4 \ln y-5 \ln z$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:06

Write the given expression…

01:10

01:03

00:44

Write the logarithms as $a…

01:26

Write the given logarithm …

01:50

00:39

Expand the logarithms as s…

01:45

00:48

02:38

Express in terms of logari…

00:34

Write logarithm as a sum. …

01:17

Condense the expression to…

Yes. Sometimes when I do a problem like this, I won't follow all of the law of logs. Um, I'll kind of tell you what what I will do. And then it should help you with the shortcut executed y to the fourth over Z to the fifth. Because sometimes what I'll do is I'll just rewrite this problem as natural log of X cubed y to the fourth Z to the negative fifth. That is Ah, true fact in math. Uh, that in denominator exponents is a negative exponents in the numerator. So what I'll do is I'll change all of my multiplication, then, uh, to be additions. So National League of Execute plus natural log of y to the fourth and then plus natural log of Z to the negative fifth. Um, that's how we split up logs using multiplication. So then, from here, what I would do is move my exponents in front so it becomes three. Natural log of X plus four natural log of X. I'm sorry. Why? And in this when I move a negative five in front well, plus a negative five will make it minus five natural Agassi. And this is your final answer. If you're looking at that and saying that's silly, why would you do it that way? Thea Other options to look at this. And when you divide by a number, you subtract instead of ad. Um, but no matter how you do it, this is the right answer right there.

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