Touch (in my opinion) logarithm simplification question

**s3a** · June 6th 2009, 06:46 PM

I keep getting 10/7 as an aswer but that isn't even one of the multiple choice!
Any help would be greatly appreciated!
Thanks in advance!

**TheEmptySet** · June 6th 2009, 07:42 PM

Originally Posted by s3a

I keep getting 10/7 as an aswer but that isn't even one of the multiple choice!
Any help would be greatly appreciated!
Thanks in advance!

You will need these log properties

$\log(xy)=\log(x)+\log(y)$ and

$\log\left( \frac{x}{y}\right)=\log(x)-\log(y)$

$\log(x^c)=c\log(x)$

$\log_{a}(a)=1$

So you have

$\log_{a}\left(\frac{x^2 a}{y} \right)=\log_{a}(x^2a)-\log_{a}(y)=$

$\log_{a}(x^2)+\log_{a}(a)-\log_{a}(y) = 2\log_{a}(x)+\log_{a}(a)-\log_{a}(y)$

I hope this helps

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