SOLUTION: 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. Please help, um sorry I couldn't write it perfectly!

Algebra ->  Exponents -> SOLUTION: 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. Please help, um sorry I couldn't write it perfectly!      Log On


   

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.
Please help, um sorry I couldn't write it perfectly!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This solution is abbreviated, because so much text to type:

log(x^2y)=p gives 2%2Alog%28x%29%2Blog%28y%29=p.
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log(xy^2)=q gives log%28x%29%2B2%2Alog%28y%29=q.
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That is a system of equations with the unknowns being log(x) and log(y). Solving with the Elimination Method will give you these:
highlight%28log%28y%29=%282q-p%29%2F3%29 and highlight%28log%28x%29=%282p-q%29%2F3%29.
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The equation you want to write all in terms of p and q is
log%28%28xy%29%5E3%29=%281%2F3%29log%28x%29%2B%281%2F3%29log%28y%29.
Now, replace log(x) and log(y) with their formulas found, and simplify.
%281%2F3%29%28%282p-q%29%2F3%29%2B%281%2F3%29%28%282q-p%29%2F3%29
highlight%28%282p-q%29%2F9%2B%282q-p%29%2F9%29