SOLUTION: This is frustrating. I've been working on this problem for too long now. It's a simple problem, but when I asked a tutor at my school for help, she said it was correct when I showe

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Question 91932: This is frustrating. I've been working on this problem for too long now. It's a simple problem, but when I asked a tutor at my school for help, she said it was correct when I showed her my answer. I was to evaluate log-base7 7^3. I divided Log7^3 by Log7 and got .8450 Another tutor told me the answer is 2, because 2 divisions are used to get to 1. now I'm lost and trying to figure this out. Which answer is it? This is my last question for the day. :o)
Answer by kev82(151) (Show Source):
You can put this solution on YOUR website!
Hi,

Ok, well I don't agree with either of the answers you've been given. I say the answer is 3.

I think your first problem is that you're not using your calculator properly. The best thing to do is to do it in bits. First put into your calculator 7^3. You should get it as 343. Then if you take the base 10 logorithm (the log button) of 343, you should get 2.53529412... Keep trying until you get this. Then take the base 10 logorithm of 7. You should get 0.84509804.... If you then divide these you will get 3 (or very close to 3).

Now try entering it all in one go. See if you can still get 3. If you don't you're doing something wrong. Your maths teacher should be able to explain how to use the calculator. (they are all different unfortunately). That's not really something I can do over the internet though.

Once you've got in working with the log button, try using the ln button. Although the numbers in the middle will be different, the answer is still 3. It doesn't matter which log you use, as long as you use the same log consistently.

You could have also used some of the fundamental properties of logorithms:

and

So

Hope that helps,

Kev