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Use $\log 2=0.3010$ and $\log 5=0.6990$ and the properties of logarithms to compute the given logarithm, do not use a calculator.$$\log 20$$

$$1.3010$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

Oregon State University

Lectures

01:24

Use $\log 2=0.3010$ and $\…

01:01

01:36

01:21

02:14

00:21

Rewrite the logarithm equa…

00:20

02:13

Use the properties of loga…

01:45

Express each logarithm in …

01:05

Use a calculator to verify…

Okay, so this problem actually needs you to use both Log of two equals that 20.3010 and log of five, which is 0.6, Let's forget 990 And my students, at least in the past, have always struggled with figuring out how to break down 20. But all I would do is just the prime factory ization. And I know some people prefer writing this out is four and five, um, four times. So I was 20 and then break down to as two times two. But even if you don't do that, the whole premise is okay, So I'm jumping from here to down here is that log of 20 is breaks down as, um, two times, two times five. Um, and then from there I mean, really, you don't have to do it my way, But this does work because trust me two times, two times five equals 20. So then, from there, I'm just thinking about Well, what we can do is do log of two, because it's multiplication. Then plus log of to. So there's two logs. It, too, would be another way of doing this. Plus log five. I don't want to show you eight different ways of doing this problem. But the whole premise, then, is I can replace the to log of 2.3010 and I can replace the log of five with 50.6990 So you're not supposed to use a calculator. But you know, at least some of my students are pretty bad with fractions. Our decimals even 0.301 plus 0.301 plus 0.699 zero, um is equal to log of 20 which is equal to when you add all that together. I don't know. Maybe this would be really easy to recognize that these two equal one. I don't know. I think we already did a problem like that. So anyway, one plus 10.301 would be 1.301 And that's your final answer, and all of the work is right here. It's kind of all over the place, though, but hopefully I did it in a step by step process that that makes sense. But that's your answer. 1.301

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