Question 240207: solve this logarithmic equation & give the exact answer.
log(base)3 (x+6) + log(base)3 (x-6) - log(base)3 x =2 Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! log(base)3 (x+6) + log(base)3 (x-6) - log(base)3 x =2
log(base)3 (x+6)(x-6) - log(base)3 x =2
log(base)3 [(x+6)(x-6)]/x =2
[(x+6)(x-6)]/x = 3^2
[(x+6)(x-6)]/x = 9
(x+6)(x-6) = 9x
x^2 - 36 = 9x
x^2 - 9x - 36 = 0
(x-12)(x+3) = 0
x = {-3, 12}
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We can throw out the -3 -- it's an extraneous solution -- leaving us with:
x = 12
