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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.$$\log 400$$

$$2.6020$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Oregon State University

Lectures

01:24

Use $\log 2=0.3010$ and $\…

01:01

02:21

01:36

01:21

02:13

Use the properties of loga…

01:45

Express each logarithm in …

00:27

Assume that $\log 4 \appro…

01:10

01:05

Use a calculator to verify…

All right. I'm gonna do this problem a little outside of the box thinking, um and it's totally acceptable because I'm within the parameter of not using my calculator. Um, and what I'm doing is I'm just thinking about that. The implied basis. 10. I'm ignoring the directions real quick where it says log of two equals longer. Five equals. You could use it that way. But what I'm gonna do is rewrite. This is a log base 10 of four times 100. I hope you agree that four times 100 is is 400. So the premise here is I can then do log based 10. 4 plus log based, 10 of 100. Okay, um, now what I'm doing is I'm just getting some decent numbers here because I know that 10 to the second power equals 100. I know some students really struggle with. Why would you do that? Well, why would I do that? Is I already know that tend to the second power is equal to 100. I just don't know what log based 10 of four is eso that's gonna bring me to my next tactic, which is doing log based 10 of two squared. So, like this is it is in and of itself. I should have written that in black. So off to the side. Now I'm going to use that tool where I know that log based too, of our sorry right down the right thing Log of to the implied basis 10. Is that 100.3010 which was given in the directions? Because as I look at this problem now, I can move this to in front, so that's equal to two times will log based 10 of two, we just figured out is or were given in the directions 20.301 and then add that to to it. Well, I think I'm ready to just give you the final answer, because if you double this, that's 0.602 And then when I add to to it, it's going to become 2.602 a lot easier than than you might originally think. That's the answer

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