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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.$$\log 10$$

$$1$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

02:21

Use $\log 2=0.3010$ and $\…

01:24

01:01

01:21

02:14

00:20

Rewrite the logarithm equa…

00:21

02:13

Use the properties of loga…

02:42

Use the base 10 exponentia…

01:45

Express each logarithm in …

00:23

Apply the properties of lo…

So if you look at this problem, the answer is obvious. If you know how to manipulate logs. So first of all, it doesn't say the answer is based. 10, but it's implied anytime you just say log of a number, um, it's implied to be based 10. Now the correct answer is thinking of 10 toe. What power would give you? 10? And that answer is one tend to the first power gives you want. Now that's not how they want you to do the problem the way they want you to do the problems. Understand that log of To is equal to point three Well, 010 and Log of five is equal to 0.699 And so the whole premise, then, is to think of it this way. I'll do this in blue. That log of 10 Well, that's equal to say in log of two times five. This is how they want you to do the problem, by the way and with the multiplication, then you can split that up as a log of two plus log of five. Well, we know that log of two is equal to that 20.3010 eso I'm replacing this log of two with 20.30 We still have a plus sign. And then we could replace this log of five with this 50.6990 And if you add those together, you get one. You're correct. Answer circled in green.

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