SOLUTION: log3(x+6)+log3(x-6)-log3x=2 solve the logarithmic equation

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Question 747802: log3(x+6)+log3(x-6)-log3x=2
solve the logarithmic equation
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2Cx%2B6%29%2Blog%283%2Cx-6%29-log%283%2Cx%29=2....in base 10 we will have
log%28x%2B6%29%2Flog%283%29%2Blog%28x-6%29%2Flog%283%29-log%28x%29%2Flog%283%29=2


%28log%28x%2B6%29%2Blog%28x-6%29-log%28x%29%29%2Flog%283%29=2
log%28x%2B6%29%2Blog%28x-6%29-log%28x%29=2log%283%29
log%28%28x%2B6%29%28x-6%29%29-log%28x%29=log%283%5E2%29
log%28%28%28x%2B6%29%28x-6%29%29%2Fx%29=log%289%29
%28%28x%2B6%29%28x-6%29%29%2Fx=9
%28x%2B6%29%28x-6%29=9x

x%5E2-6x%2B6x-36=9x
x%5E2-36=9x
x%5E2-9x-36=0..write -9x as -12x%2B3x
x%5E2-12x%2B3x-36=0....group
%28x%5E2-12x%29%2B%283x-36%29=0
x%28x-12%29%2B3%28x-12%29=0
%28x%2B3%29%28x-12%29=0
solutions:
if x%2B3=0 => x=-3
if x-12=0 => x=12

recall:
logarithm of negative number is undefined
so, your solution is only highlight%28x=12%29