SOLUTION: rewrite as a single logarithm: 2log(3x)-log(2x)+log(x-1) Solve: log(x+2)-2logx = 0

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Question 310559: rewrite as a single logarithm:
2log(3x)-log(2x)+log(x-1)

Solve:
log(x+2)-2logx = 0

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite as a single logarithm:
2log(3x)-log(2x)+log(x-1)
= log(3x)^2 + log(x-1) - log(2x)
= log[9x^2(x-1)/(2x)]
= log[(9/2)x(x-1)]
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Solve:
log(x+2)-2logx = 0
log(x+2) = 2log(x)
log(x+2) = log(x^2)
x^2 = x+2
x^2-x-2 = 0
Factor:
(x-2)(x+1)= 0
Positive solution:
x = 2
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Cheers,
Stan H.
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