Question 91932
Hi,<br />

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

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).<br />

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.<br />

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.<br />

You could have also used some of the fundamental properties of logorithms:<br />

*[tex \log_b x^y = y\log_b x] and *[tex \log_b b = 1]<br />

So *[tex \log_7 7^3 = 3\log_7 7 = 3*1 = 3]<br />

Hope that helps,<br />
Kev