# Math Help - expanding expression using properties of logarithms

1. ## expanding expression using properties of logarithms

Use the properties of logarithms to expand the expression.

Can anyone help me with this one?

2. Hello,

Ummm well, the only log properties you can use are :
$\ln(ab)=\ln(a)+\ln(b)$
$\ln \left(\frac ab \right)=\ln(a)-\ln(b)$
$\ln \left(a^b\right)=b \ln(a)$

So here we have :
$\ln \left[\frac{(3x^6+2) \sqrt{x+8}}{(x-1)^4}\right]=\ln [3x^6+2]+\ln \left[\sqrt{x+8}\right]-\ln \left[(x-1)^4\right]$
that was using the first 2 properties.

now use the last one :
$=\ln [3x^6+2]+\frac 12 \cdot \ln [x+8]-4 \ln [x-1]$

but it doesn't look more beautiful

3. oh I thought there was much more to it haha.. wow it looked more beautiful just the way it was in the beginning XD.

Thanks for the help!