expanding expression using properties of logarithms

**Kitty216** · November 20th 2008, 11:10 PM

Use the properties of logarithms to expand the expression.

Can anyone help me with this one?

**Moo** · November 21st 2008, 09:30 AM

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

**Kitty216** · November 21st 2008, 02:17 PM

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!

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