# Thread: Touch (in my opinion) logarithm simplification question

1. ## Touch (in my opinion) logarithm simplification question

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

2. 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!
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