# 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.

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#### CaptainBlack

MHF Hall of Fame
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

dwatkins741

#### 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