SOLUTION: Given that {{{(log(m,((x^2)y)))=n}}} and {{{(log(m,((x)/(y^2))))=p}}}, express {{{(log(m,(x/y)))}}} in terms of {{{n}}} and {{{p}}}.

Question 763180: Given that and , express in terms of and .
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Given that and , express in terms of n and p
----------
Given that and , express in terms of n and p (all logs same base)
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2log(x) + log(y) = n *2 --> 4log(x) + 2log(y) = 2n
log(x) - 2log(y) = p
4log(x) + 2log(y) = 2n
------------------------ Add
5log(x) = 2n + p
log(x) = (2n+p)/5
====================
2log(x) + log(y) = n
log(x) - 2log(y) = p *2 --> 2log(x) - 4log(y) = 2p
---
2log(x) + log(y) = n
2log(x) - 4log(y) = 2p
------------------------- Subtract
5log(y) = n - 2p
log(y) = (n-2p)/5
-----
log(x/y) = log(x) - log(y) = ((2n+p) + (n-2p))/5

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