SOLUTION: what is the answer for log(2x+1) = 1 + log (x-2) ?

Question 704977: what is the answer for log(2x+1) = 1 + log (x-2) ?
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what is the answer for
log(2x+1) = 1 + log (x-2)
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log(2x+1) - log(x-2) = 1
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log[(2x+1)/(x-2)] = 1
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(2x+1)/(x-2) = 10^1
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Cross-multiply
2x+1 = 10(x-2)
2x + 1 = 10x -20
8x = 21
x = 21/8
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Cheers,
Stan H.
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Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Steps:
log(2x+1)-log(x-2)=1
log((2x+1)/(x-2))=1 [property of logarithms]

You need to know which base to continue. Is the base 10, or 2, or e? If base is 10, then (2x+1)/(x-2)=10,
2x+1=10x-20,
1=8x-20
-19=8x,
x=-19/8
Is base 2?
(2x+1)=2(x-2)
2x+1=2x-4
False
Is the base e?
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