ln division question (precalc section?)

[dwatkins741]

ln division question

I have the problem
Expand:

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

Is it legal to distribute ln like this?

Here is what I got:

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

Thanks.

 

[CaptainBlack]

I have the problem
Expand:

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

Is it legal to distribute ln like this?

Here is what I got:

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

Thanks.

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

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

CB

 

[Sudharaka]

I have the problem
Expand:

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

Is it legal to distribute ln like this?

Here is what I got:

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

Thanks.

Dear dwatkins,

\(\displaystyle \ln{(a\times{b})}=\ln{(a)}+\ln{(b)}~but~\ln(a+b)\neq{\ln{(a)}+\ln{(b)}}\)

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

Hope this will help you.