SOLUTION: If {{{ log(3,N) = x}}} and {{{ log(15,N) = y}}}, prove that {{{log(45,5) = (x-y)/(x+y)}}} Thanks

Algebra ->  Equations -> SOLUTION: If {{{ log(3,N) = x}}} and {{{ log(15,N) = y}}}, prove that {{{log(45,5) = (x-y)/(x+y)}}} Thanks      Log On


   

Question 976044: If +log%283%2CN%29+=+x and +log%2815%2CN%29+=+y, prove that log%2845%2C5%29+=+%28x-y%29%2F%28x%2By%29
Thanks
Answer by JoelSchwartz(130) About Me  (Show Source):
You can put this solution on YOUR website!
3^x=N
15^y=N
3^x=15^y
3^(x/y)=15
10^(log(3))=3
10=3^(1/(log(3)))
10^(log(15))=15
(3^(1/(log(3))))^(log(15)=15
3^((log(15))/(log(3)))=15
x/y=(log(15))/(log(3))
x=log(15)
y=log(3)
45^((log(15)-log(3))/(log(15)+log(3)))=5
45^((log(5))/(log(45)))=5