document.write( "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 $\"p\"$ . \n" ); document.write( "

Algebra.Com's Answer #464609 by Alan3354(69443) $\"\"$ $\"About$

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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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\n" ); document.write( "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)
\n" ); document.write( "-----------
\n" ); document.write( "2log(x) + log(y) = n *2 --> 4log(x) + 2log(y) = 2n
\n" ); document.write( "log(x) - 2log(y) = p
\n" ); document.write( "4log(x) + 2log(y) = 2n
\n" ); document.write( "------------------------ Add
\n" ); document.write( "5log(x) = 2n + p
\n" ); document.write( "log(x) = (2n+p)/5
\n" ); document.write( "====================
\n" ); document.write( "2log(x) + log(y) = n
\n" ); document.write( "log(x) - 2log(y) = p *2 --> 2log(x) - 4log(y) = 2p
\n" ); document.write( "---
\n" ); document.write( "2log(x) + log(y) = n
\n" ); document.write( "2log(x) - 4log(y) = 2p
\n" ); document.write( "------------------------- Subtract
\n" ); document.write( "5log(y) = n - 2p
\n" ); document.write( "log(y) = (n-2p)/5
\n" ); document.write( "-----
\n" ); document.write( "log(x/y) = log(x) - log(y) = ((2n+p) + (n-2p))/5
\n" ); document.write( " $\"log%28m%2Cx%2Fy%29+=+%283n-p%29%2F5\"$
\n" ); document.write( " \n" ); document.write( "

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