Use the properties of logarithms to expand the expression.
Can anyone help me with this one?
Hello,
Ummm well, the only log properties you can use are :
$\displaystyle \ln(ab)=\ln(a)+\ln(b)$
$\displaystyle \ln \left(\frac ab \right)=\ln(a)-\ln(b)$
$\displaystyle \ln \left(a^b\right)=b \ln(a)$
So here we have :
$\displaystyle \ln \left[\frac{(3x^6+2) \sqrt{x+8}}{(x-1)^4}\right]=\ln [3x^6+2]+\ln \left[\sqrt{x+8}\right]-\ln \left[(x-1)^4\right]$
that was using the first 2 properties.
now use the last one :
$\displaystyle =\ln [3x^6+2]+\frac 12 \cdot \ln [x+8]-4 \ln [x-1]$
but it doesn't look more beautiful