Question 1020327: log (2x+1) = 1-log (x-2)
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Let's rearrange this and use the laws of logs...so from
log(2x+1) = 1 - log(x-2)
log(2x+1) + log(x-2) = 1
log[(2x+1)(x-2)] = 1
Now exponentiating 10-to-the
(2x+1)(x-2) = 10
2x^2 - 3x - 2 = 10
2x^2 - 3x - 12 = 0
Solve using quadratic formula to get
x = 3.31 and x = -1.81
Second root is extraneous, so
x = 3.31
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