Question

given that \[\log_{a}(x/y)=4.5\] and \[\log_{a}x^{5}y^{2}=5\], find the value of \[\log_{a}\sqrt{xy}\]

Answer 1

start with
\[\log(x)-\log(y)=4.5\]
\[5\log(x)+2\log(y)=5\] then solve the system of equations in log(x) and log(y)

Answer 2

just like solving
\[x-y=4.5\]
\[5x+2y=5\] only with log(x) instead of x and log(y) instead of y.
you will get
\[\log(x)=2,\log(y)=-2.5\]
http://www.wolframalpha.com/input/?i=x-y%3D4.5+and+5x%2B2y%3D5

Answer 3

then
\[\log(\sqrt{xy})=\frac{1}{2}(\log(x)+\log(y))\]
plug in the numbers, get out your answer

Answer 4

:'D th-thank you!

Answer 5

i dont understand how you got log(x)=2,log(y)=−2.5 can you explain?

Answer 6

wait it's log base a