SOLUTION: What is the exact answer of log(x+2)+log(x-3)=log(4x)

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Question 926058: What is the exact answer of log(x+2)+log(x-3)=log(4x)
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the exact answer of log(x+2)+log(x-3)=log(4x)
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log%28%28x%2B2%29%2A%28x-3%29%29+=+log%284x%29
%28x%2B2%29%2A%28x-3%29+=+4x
Now it's a quadratic.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%2B2%29%2Blog%28x-3%29=log%284x%29
log%28%28x%2B2%29%28x-3%29%29=log%284x%29...since log same, we have
%28x%2B2%29%28x-3%29=4x...solve for x
x%5E2-3x%2B2x-6=4x
x%5E2-x-6=4x
x%5E2-x-6-4x=0
x%5E2-5x-6=0
x%5E2%2Bx-6x-6=0
%28x%5E2%2Bx%29-%286x%2B6%29=0
x%28x%2B1%29-6%28x%2B1%29=0
%28x-6%29%28x%2B1%29=0
solutions:
if %28x-6%29=0=> highlight%28x=6%29 (real solution)
if %28x%2B1%29=0=> highlight%28x=-1%29 (assuming a complex-valued logarithm)
intersection point: (x,y)
if x=6
log%2810%2C4x%29=log%2810%2C4%2A6%29=log%2810%2C24%29=1.38=> y=1.38
(6,1.38)