SOLUTION: Solve the simultaneous equations. log base 9 (xy^2) = 1/2 (log base 3 x) (log base 3 y) = -3

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Question 1072776: Solve the simultaneous equations.
log base 9 (xy^2) = 1/2
(log base 3 x) (log base 3 y) = -3
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Change-Base formula and rules for logs will give the system

system%28log%283%2Cx%29%2B2%2Alog%283%2Cy%29=1%2Clog%283%2Cx%29log%283%2Cy%29=-3%29

For temporary symbolic convenience, you can make substitutions for log%283%2Cx%29 and log%283%2Cy%29 and solve first in your new variables, and then back-substitute to continue.

-
system%28log%283%2Cy%29=3%2F2%2Cor%2Clog%283%2Cy%29=-1%29
.
system%28y=3%5E%283%2F2%29%2Cor%2Cy=1%2F3%29
.
.