SOLUTION: Please help me solve this equation: {{{log base a b^2*log base b a^3=6}}}

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Question 926737: Please help me solve this equation: log+base+a+b%5E2%2Alog+base+b+a%5E3=6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%28a%2Cx%29 can be converted to the base b by the formula log%28b%2Cx%29+%2Flog%28b%2Ca%29

log+%28+a%2C+b%5E2%29%2Alog%28+b%2C+a%5E3%29=6...use the formula log%28b%2Cx%29+%2Flog%28b%2Ca%29

%28log+%28+b%2C+b%5E2%29%2Flog%28+b%2C++a%29%29%2Alog%28+b%2C++a%5E3%29=6
%282log+%28+b%2C+b%29%2Fcross%28log%28+b%2C++a%29%29%29%2A3cross%28log%28+b%2C++a%29%29=6
2%28log+%28+b%2C+b%29%29%2A3=6..........log+%28+b%2C+b%29=1
2%2A3=6
6=6