I just began Logarithms and I'm a little confused... Can someone please help me? I'm posting the question in the comments.

Question

anonymous · Answer

$$\log_{3} 243$$

anonymous · Answer

How is this read? Log of 3 and what?

wolf1728 · Answer

Wow you are just beginning logarithms and already they give you a question about base 3 logs?
I think that is read the base 3 log of 243

anonymous · Answer

okay, I wasn't sure

wolf1728 · Answer

Now let's see how to calculate the base 3 log of 243
1 way to do it is with Excel (or even better the free online spreadsheet at openoffice.com

wolf1728 · Answer

and the answer is 5

wolf1728 · Answer

The base 3 log of 243 is 5 because 3^5 is 243.

anonymous · Answer

is there a way to write that out? Like to show my work.. Also, there's something about change of bases... I'm not sure how to do that either.

wolf1728 · Answer

Not to change the subject but I think the easiest way to approach logs is with base 10 logs.

anonymous · Answer

what's that?

wolf1728 · Answer

Okay well you just saw a base 3 log right?

anonymous · Answer

yeah

wolf1728 · Answer

So, let's look at the powers of 10
10^1 = 10
10^2 = 100
10^3 = 1,000
10^4 = 10,000

wolf1728 · Answer

Now if we wanted to know the base 10 logarithm of 100 it would be 2, because 2 is the exponent of 10^2

anonymous · Answer

I think the thing you're talking about is for this problem: $$\log_{b} 1000=3$$

wolf1728 · Answer

That would be the base 10 log of 1,000 - yes

anonymous · Answer

okay, so it would be 3?

anonymous · Answer

I'm confused...

wolf1728 · Answer

yes the base 10 log of 1,000 is 3

anonymous · Answer

what would b equal? The choices are 0, 10, 100, 1000

wolf1728 · Answer

yes, I'm not surprised you are confused.  Is this the first time you are learning about logarithms?
I think you could find the answer to that question - want to try?

anonymous · Answer

yes, it is the first... I think it might be 100 butthat's just a guess

anonymous · Answer

oh wait....... Is it 10 because 10^3 = 1000?

wolf1728 · Answer

The answer is right on this page. A few posts ago I said that the base 10 log of 1000 is 3 - and you got it right!!!

anonymous · Answer

Yay! by the way the explanation is written like this:
|dw:1377456906909:dw|
(these are the practice problems)
Is that how it's done?