SOLUTION: log (2-3x) - log x = log 2x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log (2-3x) - log x = log 2x      Log On


   

Question 37816: log (2-3x) - log x = log 2x
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+log%282-3x%29+-+log%28x%29+=+log%282x%29+
+log%28%282-3x%29%2Fx%29+=+log%282x%29+

and now raise both sides to power 10:
+%282-3x%29%2Fx+=+2x+
+2-3x+=+2x%5E2+
+2x%5E2+%2B+3x+-+2+=+0+
(2x - 1)(x + 2) = 0
so 2x-1 = 0 or x+2 = 0
so x=1/2 or x=-2

CHECK:
put x=1/2 into +log%282-3x%29+-+log%28x%29+=+log%282x%29+ and all th elog terms are fine.

put x=-2 into +log%282-3x%29+-+log%28x%29+=+log%282x%29+ and we get +log%288%29+-+log%28-2%29+=+log%28-4%29+

and the last 2 log terms are not defined for this. So the answer to the question is x=1/2.

jon.