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}}}.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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}}}.      Log On


   

Question 763180: Given that %28log%28m%2C%28%28x%5E2%29y%29%29%29=n and %28log%28m%2C%28%28x%29%2F%28y%5E2%29%29%29%29=p, express %28log%28m%2C%28x%2Fy%29%29%29 in terms of n and p.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that log%28m%2C%28%28x%5E2%29y%29%29=n and log%28m%2C%28%28x%29%2F%28y%5E2%29%29%29=p, express log%28m%2C%28x%2Fy%29%29 in terms of n and p
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Given that log%28x%5E2y%29=n and log%28x%2Fy%5E2%29=p, express log%28x%2Fy%29 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
log%28m%2Cx%2Fy%29+=+%283n-p%29%2F5