# Homework Help: Simplifying Expression using Logarithms

1. Jun 12, 2010

Simplify the attached expression using any relevant logarithmic rules

I havent really done much with logarithms, so i didnt know where to start?

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2. Jun 12, 2010

### rl.bhat

Given problem can be written as

log(2)4 + log(16)1/4 + log(1/4)2 - log(7/4)

Now use laws of logarithm to simplify.

3. Jun 12, 2010

the problem is I dont know how to do that?

4. Jun 12, 2010

### rl.bhat

log(a) + log(b) = log(ab)

log(a) - log(b) = log(a/b)

5. Jun 12, 2010

### HallsofIvy

Then you should start by learning the "relevant logarithmic rules"!

$log(ab)= log(a)+ log(b)$

$log(a/b)= log(a)- lob(b)$

$log(a^b)= b log(a)$

6. Jun 12, 2010

Can somebody please demonstrate the question?

7. Jun 12, 2010

### Tedjn

No, you need to solve it yourself; you received sufficient help in the previous posts. Follow that advice.

8. Jun 12, 2010

That advice dosent get me anywhere!

9. Jun 12, 2010

### Tedjn

Post what you have tried so far pertaining to the advice, or post and ask a question regarding the advice. If I asked you to simplify log(a) + log(b), how would you do it?

10. Jun 12, 2010

well that would be log(ab)

11. Jun 12, 2010

### Tedjn

Yes, so look at the 3 logarithm rules provided by HallsofIvy and apply them to your problem.

12. Jun 12, 2010

ok so I'm up to log(2^2) + log(16^1/4) + log(1/4^2) - log(7/4)

13. Jun 12, 2010

### Tedjn

Instead of log(22) it should be something else. Now, continue until you get an expression with only one log.

14. Jun 12, 2010

yes ok it would be log(2^4), but then I realy am stuck on what to do next!

15. Jun 12, 2010

### Tedjn

16. Jun 12, 2010

I dont know how to!!!!!!

17. Jun 12, 2010

### rl.bhat

OK.

What is 24, 161/4 and 42?

Substitute these values in my post #2 and simplify by using the relevant equation given by us.

18. Jun 12, 2010

19. Jun 12, 2010

Ok, now I have one which is attached.
I have managed to get to this
logx4/logx1/3
What do I do from here?

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20. Jun 12, 2010