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

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

Algebra.Com

Question 976044: If and , prove that
Thanks
Answer by JoelSchwartz(130) (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

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