Question

I'm studying logarithms right now, and having a lot of trouble with simplifying the expressions. Right now what I really need help with is changing the base, I'm not understanding how the textbook is getting to the answers despite having the steps kind of shown to me. Here is an example of the problem solved for me, and the one that I need to solve.

Solved in textbook: log(4)8=log(2)8/log(2)4=3/2
It said to change to a base of 2, because 2 is a power of both 4 and 8. I used about 6 different calculators and could not get to that answer of 3/2.

Need to solve: log(8)16

Answer 1

The reason you are having trouble with logarithms is that you aren't meant to use a calculator at this point. That being said, you can still use a calculator to solve the problem, but not in the same way.

Answer 2

Well, the teacher and the book both say that I can use one; however, I was not using it to try to solve, but rather to try and see how they arrived at the answer of 3/2. Until I know that, I can't move on to solving the actual problem that I need to.

Answer 3

have you learned the base change law of logarithms yet? also, does the whole idea of a logarithm make sense to you intuitively right now?

Answer 4

That is the exact thing we are studying right now, that's why I have to solve these problems.

Answer 5

Not really.. Math in general is hard for me, algebra is my worst math subject, and logarithms are extremely confusing. I get how to change the base, I think, like in the problem that I have to solve I could also use 2, because it is a power of both 8 and 16. I just don't get how to arrive at that answer.

Answer 6

so, if you can spare 30minutes to an hour I can explain the whole concept from scratch so hopefully it makes more sense to you. Do you have the time?

Answer 7

Unfortunately not really, I just want to know how to do this one thing so I can move on and finish the lesson for the night.

Answer 8

I appreciate the offer really, but I'll be consulting with my teacher next week on everything else I need help with. :)

Answer 9

lol, my advice to you would be to spend a bit of time learning it before you're lost in the dust, but it doesn't really matter. @physicscrap , would you do me a favor and take it from here?

Answer 10

im assuming you mean log base of 4 here log(4)8, would be log(16)/log(8). which are log base 10. default.

Answer 11

my bad

Answer 12

Yes it's a base of 4, that's the only way that I can write it.

Answer 13

for log(8)16, we can split that up into bases of 10, log(16)/log(8) = 3/2, does that help?

Answer 14

I don't really understand what you did there.

Answer 15

3/2 is also not one of the possible answers for that problem. :/

Answer 16

8^1.33333 = 16

Answer 17

on your calculator, use the default log with a base of 10. log(16) divided by log(8) and thats what log base8(16) is equal to.

Answer 18

So whatever power I raise the base to to get to 16 (or whatever answer) is the answer? Because I just tried that with the second question (log(9)27) and got 1.5, and got it right.

Answer 19

That seems like a much easier way of doing things. :)

Answer 20

you good? or any other questions?

Answer 21

Nope, I can manage from here! Thanks.