SOLUTION: solve 2log X- log(X-2) =2 log 3

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Question 1029334: solve 2log X- log(X-2) =2 log 3
Answer by ikleyn(52797) About Me  (Show Source):
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solve 2log X- log(X-2) =2 log 3
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2*log(x) - log(x-2) = 2*log(3)  --->

log%28%28x%5E2%29%29 - log%28%28x-2%29%29 = log%28%283%5E2%29%29  --->

log%28%28x%5E2%2F%28x-2%29%29%29 = log%28%289%29%29  --->

x%5E2%2F%28x-2%29 = 9,           (next step is to multiply both sides by (x-2) to rid off the denominator)

x%5E2 = 9%2A%28x-2%29         (next step is to simplify)

x%5E2+-+9x+%2B+18 = 0,       (next step is to factor the left side)

(x-3)*(x-6) = 0.

The roots of the last equation are  x = 3  and  x = 6.

They both satisfy the original equation. Check it !

Answer.  x = 3  and  x = 6.