SOLUTION: Solve log(x-1)- log6 = log(x-2)- logx

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Question 105760: Solve log(x-1)- log6 = log(x-2)- logx
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x-1%29-+log%286%29+=+log%28x-2%29-+log%28x%29
log%28%28x-1%29%2F%286%29%29=log%28%28x-2%29%2F%28x%29%29
%28x-1%29%2F%286%29=%28x-2%29%2F%28x%29


By cross multiplication,
6%28x%2B2%29=x%28x-1%29
6x%2B12=x%5E2-x
x%5E2-x=6x%2B12
x%5E2-x%2Bx=6x%2Bx%2B12
x%5E2=7x%2B12
x%5E2-7x=7x-7x%2B12
x%5E2-7x=12
x%5E2-7x-12=12-12
x%5E2-7x-12=0

By the quadratic formula,
x=%287%2B-sqrt%287%5E2-4%2A1%2A%28-12%29%29%29%2F%282%2A1%29
x=%287%2B-sqrt%2849%2B48%29%29%2F%282%29
x=%287%2B-sqrt%2897%29%29%2F%282%29
x=%287%2B+sqrt%2897%29%29%2F%282%29 or x=%287-+sqrt%2897%29%29%2F%282%29

Power up,
HyperBrain!