SOLUTION: What is the domain of the logarithmic equation? log(3x+1)(x-2)

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Question 534433: What is the domain of the logarithmic equation? log(3x+1)(x-2)
Found 2 solutions by solver91311, fcabanski:
Answer by solver91311(24713) About Me  (Show Source):
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I don't see a logarithmic equation anywhere. In fact, I don't see an equation anywhere. Equations have equals signs in them. The domain of a log function in general is the set of values such that the argument of the log is greater than zero.

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Answer by fcabanski(1391) About Me  (Show Source):
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The log function log (x) is defined for only x>0.


For this one it's like an equation that must be > 0.


(3x+1)(x-2)>0 by the zero product rule both must be > 0.


3x+1 >0 subtract 1 from both sides 3x >-1 divide both sides by 3. x > -1/3


x-2 > 0 add 2 to both sides. x > 2


The domain is (2, infinity) since any x = 2 or x<2 will make (x-2) <= 0 and thus will make the function undefined.