document.write( "Question 841605: Given that log[base 7](x^2)y = p and log[base 7]xy^2 = q, find log[base 7]cubicroot(xy) in terms of p and q.\r
\n" ); document.write( "\n" ); document.write( "Please help, um sorry I couldn't write it perfectly! \n" ); document.write( "

Algebra.Com's Answer #507051 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
This solution is abbreviated, because so much text to type:\r
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\n" ); document.write( "\n" ); document.write( "log(x^2y)=p gives $\"2%2Alog%28x%29%2Blog%28y%29=p\"$ .
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\n" ); document.write( "log(xy^2)=q gives $\"log%28x%29%2B2%2Alog%28y%29=q\"$ .
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\n" ); document.write( "That is a system of equations with the unknowns being log(x) and log(y). Solving with the Elimination Method will give you these:
\n" ); document.write( " $\"highlight%28log%28y%29=%282q-p%29%2F3%29\"$ and $\"highlight%28log%28x%29=%282p-q%29%2F3%29\"$ .
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\n" ); document.write( "The equation you want to write all in terms of p and q is
\n" ); document.write( " $\"log%28%28xy%29%5E3%29=%281%2F3%29log%28x%29%2B%281%2F3%29log%28y%29\"$ .
\n" ); document.write( "Now, replace log(x) and log(y) with their formulas found, and simplify.
\n" ); document.write( " $\"%281%2F3%29%28%282p-q%29%2F3%29%2B%281%2F3%29%28%282q-p%29%2F3%29\"$
\n" ); document.write( " $\"highlight%28%282p-q%29%2F9%2B%282q-p%29%2F9%29\"$ \n" ); document.write( "

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