SOLUTION: Solve for x and check: 2 ln (x) = ln (x+6)

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Question 867068: Solve for x and check:
2 ln (x) = ln (x+6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Aln%28x%29+=+ln%28x%2B6%29


ln%28x%5E2%29+=+ln%28x%2B6%29


e%5E%28ln%28x%5E2%29%29%5E%22%22+=+e%5E%28ln%28x%2B6%29%29%5E%22%22


x%5E2+=+x%2B6


x%5E2-x-6=0


%28x-3%29%28x%2B2%29=0


x-3=0 or x%2B2=0


x=3 or x=-2


The domain of ln%28x%29 is x%3E0, so we toss out x=-2 since that's negative.


The only solution is x=3


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Check:


2%2Aln%28x%29+=+ln%28x%2B6%29


2%2Aln%283%29+=+ln%283%2B6%29


2%2Aln%283%29+=+ln%289%29


ln%283%5E2%29+=+ln%289%29


ln%289%29+=+ln%289%29 Solution is verified.