SOLUTION: log(6)^x+log(6)^(x-9)=2 How do I solve for x? please help

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Question 579298: log(6)^x+log(6)^(x-9)=2
How do I solve for x?
please help
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Your notation is confusing. I'll assume you meant log base 6:
log%286%2Cx%29%2Blog%286%2C%28x-9%29%29=2
log%286%2Cx%28x-9%29%29=2
x%28x-9%29=6%5E2
x%5E2-9x=36
x%5E2-9x-36=0
%28x-12%29%28x%2B3%29=0
x = {-3, 12}
But, since you can't take the log of a negative number, the -3 is an extraneous answer -- throw it out leaving:
x = 12