# True or False?

• Jun 29th 2011, 05:36 PM
Googl
True or False?
Hi all,

In this true or false?

(5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)
• Jun 29th 2011, 05:39 PM
Krizalid
Re: True or False?
$a-b=-b+a,$ it's true, haha. :D
• Jun 29th 2011, 05:45 PM
Sudharaka
Re: True or False?
Quote:

Originally Posted by Googl
Hi all,

In this true or false?

(5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)

Dear Googl,

The equation is false. Substitute x=1.

$\mbox{R.H.S}=0$

$\mbox{L.H.S}=\frac{5i \pi}{2}$
• Jun 29th 2011, 05:54 PM
Krizalid
Re: True or False?
Oh, I misread it, I thought it was $1-2x$ on both sides.
• Jun 29th 2011, 05:57 PM
Googl
Re: True or False?
One of them is the correct result of an integration using partial fractions. For some reason (I don't know) some of the results are in this form -2ln(x)+(5/2)ln(2x-1) however the first one: (5/2)ln(1-2x)-2ln(x), note there is a pattern (2x-1) instead of (1-2x).

This was for the integration of:

(x+2)/(2x^2-x)

Is there something I need to understand here?
• Jun 29th 2011, 05:58 PM
Krizalid
Re: True or False?
Remember to put absolute value to the logarithm.