1. Looking for Solution Feedback

Could someone please review this problem that I have attempted to simplify. I'm not sure but I believe that I have completed everything correctly.

$log_{5}\frac{5^{-2x} (25)^y}{\sqrt{125^x}}$

$\Rightarrow\log_{5}5^{-2x}+\log_{5}25^{y}-\log_{5}\sqrt{125^{x}}$

$\Rightarrow\text{-}2x\log_{5}5+2y\log_{5}5-\frac{3x}{2}\log_{5}5$

$\Rightarrow\text{-}2x+2y-\frac{3x}{2}$

$\Rightarrow\frac{-7x}{2}+2y$

Any feedback is appreciated.

2. Originally Posted by headless chickens
Could someone please review this problem that I have attempted to simplify. I'm not sure but I believe that I have completed everything correctly.

$log_{5}\frac{5^{-2x} (25)^y}{\sqrt{125^x}}$

$\Rightarrow\log_{5}5^{-2x}+\log_{5}25^{y}-\log_{5}\sqrt{125^{x}}$

$\Rightarrow\text{-}2x\log_{5}5+2y\log_{5}5-\frac{3x}{2}\log_{5}5$

$\Rightarrow\text{-}2x+2y-\frac{3x}{2}$

$\Rightarrow\frac{-7x}{2}+2y$

Any feedback is appreciated.
looks fine to me.

3. Originally Posted by skeeter
looks fine to me.
Thanks again for your time .... always nice to have someone else check your work once in a while.