# Simplifying Expression using Logarithms

rl.bhat
Homework Helper
just one more question, how do I simplify this and express with positive indices.
(18x^3 X 2x^-4)/(4x^-5 X 6x)
$$\frac{36x^3}{x^4}\times\frac{24x}{x^5}$$

Now simplify.

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could someone plese show a bit more detail with the second problem, where did 12 come from.

rl.bhat
Homework Helper
could someone plese show a bit more detail with the second problem, where did 12 come from.

= $$\frac{4\times3\log{x}}{\log{x}}$$

Now siplify.

I missed the step before that. wheres the 3 come from?

Sorry im really bad at this.

rl.bhat
Homework Helper
I missed the step before that. wheres the 3 come from?

Sorry im really bad at this.
$$\frac{1}{\frac{1}{3}\log{x}} = \frac{3}{\log{x}}$$

Ok i think i got it now. i got it down to 12 by doing this:

2Logx^2 / 1/3Logx
= 4Logx / 1/3Logx
=4 * 3Logx / Logx
=12Logx / Logx
=12

is all the working out correct? if not can u show me the full question with working, all set out as if it were a test?

rl.bhat
Homework Helper
Ok i think i got it now. i got it down to 12 by doing this:

2Logx^2 / 1/3Logx
= 4Logx / 1/3Logx
=4 * 3Logx / Logx
=12Logx / Logx
=12

is all the working out correct? if not can u show me the full question with working, all set out as if it were a test?
Yes. It is correct.

cool, but now, back to the first question.

i got up to:
Log(2^4) + Log(16^1/4) + Log(1/4^2)
= Log 16 + Log 4 + Log 0.0625 - Log 1.75
Is this correct?

Then would it go:
Log(16 x 4 x 0.0625) = Log4
= Log(4/1.75)
So y have i got 4/1.75, and jahaddo has 2/1.75??