Logs

[Timcago]

Let log(base a)^x=-5, log(base a)^y=2, and log(base a)^z=.25. Find the values of the following.

1. log(base a)^((xy^2)/(z^3))^2

Here was my attempt:

2(log(base a)^x+2log(base a)^y-3log(base a)^z)

2(-5+2(2)-3(.25)) *<-do i multiply 3 by .25 or take .25 to the 3rd power?*
2(-5+4-.75)
=-3.5

Is that right?

 

[galactus]

\(\displaystyle \L\\log_{a}x=-5; log_{a}y=2; log_{a}z=\frac{1}{4}\)

\(\displaystyle \L\\log_{a}(\frac{xy^{2}}{z^{3}})^{2}=\\

2(log_{a}xy^{2}-log_{a}z^{3})=\\

2(log_{a}x+log_{a}y^{2})-2log_{a}z^{3}=\\

2(log_{a}x+2log_{a}y)-6log_{a}z=\\

2(-5+2(2))-6(\frac{1}{4})=\frac{-7}{2}\)

 

[Timcago]

Good deal, we got the same answer (-7/2)=-3.5