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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.$$\log 25$$

$$1.398$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Oregon State University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:01

Use $\log 2=0.3010$ and $\…

02:21

01:36

01:24

01:21

02:14

00:20

Rewrite the logarithm equa…

00:21

02:13

Use the properties of loga…

01:18

Write $\frac{1}{2} \log 25…

00:13

Rewrite each expression as…

01:45

Express each logarithm in …

00:15

Rewrite the given logarith…

So in this problem, they go ahead and give you a few clues. The clue that we care about this problem is log of five is equal to zero point 6990 If you don't believe that, then, uh, type that into your calculator, you'll see the answer, or you use that to simplify log of 25. Now, my goal is to somehow get to log of five. So what you're going to see me do is think of a number that somehow manipulates to get to five. Well, from 5 to 25. And it's true that five squared is 25. You know, I was saying, Well, why would you do that? Well, now I can use a lot of logs. That tells me I could move that exponents in front. So it's two times log of five. And now we're about ready for our final answer because we have two times log of five. Well, now we can substitute. We can replace log of five with this 50.6990 and, uh, whether you could do that in your head or you need a calculator, that final answer would be 1.3980 pitching. There you go. Yeah,

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