SOLUTION: ln(x+5)+ln(x-2)=2ln(x)

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Question 243562: ln(x+5)+ln(x-2)=2ln(x)
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%2B5%29%2Bln%28x-2%29=2ln%28x%29 Start with the given equation.


ln%28x%2B5%29%2Bln%28x-2%29=ln%28x%5E2%29 Rewrite the log on the right using the identity y%2Aln%28x%29=ln%28x%5Ey%29


ln%28%28x%2B5%29%28x-2%29%29=ln%28x%5E2%29 Combine the logs on the left using the identity ln%28A%29%2Bln%28B%29=ln%28A%2AB%29


%28x%2B5%29%28x-2%29=x%5E2 Raise both sides as powers of 'e' to eliminate the logs.


x%5E2%2B3x-10=x%5E2 FOIL


3x-10=0 Subtract x%5E2 from both sides.


3x=0%2B10 Add 10 to both sides.


3x=10 Combine like terms on the right side.


x=%2810%29%2F%283%29 Divide both sides by 3 to isolate x.


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Answer:

So the solution is x=10%2F3 which approximates to x=3.333.