# ln division question (precalc section?)

• May 26th 2010, 05:01 AM
dwatkins741
ln division question
I have the problem
Expand:

$4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)$

Is it legal to distribute ln like this?

Here is what I got:

$4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)$

Thanks.
• May 26th 2010, 06:31 AM
CaptainBlack
Quote:

Originally Posted by dwatkins741
I have the problem
Expand:

$4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)$

Is it legal to distribute ln like this?

Here is what I got:

$4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)$

Thanks.

No, you can see that by applying the laws of logarithms to

$\left(\frac{2\ln(x)+\ln(3)}{2}\right)=\left( \frac{\ln(3x^2)}{2}\right) \ne \left(\frac{\ln(x^2+3)}{2}\right)$

CB
• May 26th 2010, 06:38 AM
Sudharaka
Quote:

Originally Posted by dwatkins741
I have the problem
Expand:

$4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)$

Is it legal to distribute ln like this?

Here is what I got:

$4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)$

Thanks.

Dear dwatkins,

$\ln{(a\times{b})}=\ln{(a)}+\ln{(b)}~but~\ln(a+b)\n eq{\ln{(a)}+\ln{(b)}}$

You could find more information about identities of logarithms at, List of logarithmic identities - Wikipedia, the free encyclopedia