SOLUTION: log (2x+5)+log (x+1)=1

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Question 326418: log (2x+5)+log (x+1)=1
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%282x%2B5%29%29%2Blog%28%28x%2B1%29%29=1
log%28%282x%2B5%29%28x%2B1%29%29=1
%282x%2B5%29%28x%2B1%29=10
Use the FOIL method,
2x%5E2%2B2x%2B5x%2B5=10
2x%5E2%2B7x-5=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+
x+=+%28-7+%2B-+sqrt%28+49%2B40%29%29%2F4+
x+=+%28-7+%2B-+sqrt%28+89%29%29%2F4+
Use only the positive result since log function requires positive arguments.
highlight%28+x=%28-7%2Bsqrt%2889%29%29%2F4%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the logs is the log of the product.





Use the definition of the logarithm function:



Hence



Solve the quadratic:



Exclude any roots that would make or outside the domain of the log function. That is to say, for either of the roots of the following criteria must be met: and .

John