SOLUTION: Solve for x: log(2x-3)=logx+log(x-2) thanks.

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Question 202237: Solve for x: log(2x-3)=logx+log(x-2) thanks.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%282x-3%29+=+Log%28x%29%2BLog%28x-2%29 Apply the "product rule" for logarithms to the right side of the equation. Log%5Bb%5D%28M%2AN%29+=+Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29
Log%282x-3%29+=+Log%28%28x%29%2A%28x-2%29%29 Simplify the argument on the right side.
Log%282x-3%29+=+Log%28x%5E2-2x%29 Apply the "identity" property.:If Log%5Bb%5D%28M%29+=+Log%5Bb%5D%28N%29 then M+=+N
2x-3+=+x%5E2-2x Form into a standard quadratic equation.
x%5E2-4x%2B3+=+0 Factor.
%28x-1%29%28x-3%29+=+0 Apply the "zero product" rule.
x-1+=+0 or x-3+=+0 therefore:
highlight%28x+=+1%29 or highlight%28x+=+3%29