Question 763180
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
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Given that {{{log(x^2y)=n}}} and {{{log(x/y^2)=p}}}, express {{{log(x/y)}}} 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
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2log(x) + log(y) = n
log(x) - 2log(y) = p *2 --> 2log(x) - 4log(y) = 2p
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2log(x) + log(y) = n
2log(x) - 4log(y) = 2p
------------------------- Subtract
5log(y) = n - 2p
log(y) = (n-2p)/5
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log(x/y) = log(x) - log(y) = ((2n+p) + (n-2p))/5
{{{log(m,x/y) = (3n-p)/5}}}