# Simplifying Expression using Logarithms

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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## Answers and Replies

rl.bhat
Homework Helper
Simplify the attached expression using any relevant logarithmic rules

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

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.

the problem is I dont know how to do that?

rl.bhat
Homework Helper
the problem is I dont know how to do that?

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

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

HallsofIvy
Science Advisor
Homework Helper
Simplify the attached expression using any relevant logarithmic rules

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

the problem is I dont know how to do that?
Then you should start by learning the "relevant logarithmic rules"!

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

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

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

Can somebody please demonstrate the question?

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

That advice dosent get me anywhere!

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?

well that would be log(ab)

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

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

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

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

well that would be log(ab)

Follow your own advice. I dont know how to!!!!!!

rl.bhat
Homework Helper
I dont know how to!!!!!!

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.

Would the answer be log(2/1.75)

Or would it be 12logx? I dont know.

rl.bhat
Homework Helper
Or would it be 12logx? I dont know.

Your answer for the first problem is correct. But write it as a single number, not in the form of a fraction.

In the second problem from where did you get log(x) along with 12?

The second problem, I worked out to be just 12 now. But the first problem, 2/1.75 equals a long decimal, so wouldnt I just leave it as a fraction?

rl.bhat
Homework Helper
The second problem, I worked out to be just 12 now. But the first problem, 2/1.75 equals a long decimal, so wouldnt I just leave it as a fraction?

In that case you can write it as 8/7

Thankyou Very Much! :D

just one more question, how do I simplify this and express with positive indices.
(18x^3 X 2x^-4)/(4x^-5 X 6x)