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

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) (Show Source): You can put this solution on YOUR website!

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.

John

My calculator said it, I believe it, that settles it

Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
Check my profile and contact me for one on one online tutoring.

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.

RELATED QUESTIONS
What is the domain of this logarithmic function? y=-2 log x (answered by ikleyn)
what is the domain of this logarithmic function f(x)-log... (answered by Boreal)
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of... (answered by edjones)
Kindly explain how to resolve the following logarithmic equation 1) 1 - log (x - 2) =... (answered by Earlsdon,Alan3354)
Find the domain and solve the following logarithmic equation log^2 *with base 2,... (answered by MathLover1,greenestamps)
find the domain of the logarithmic function log 3 (2x+2)+log 3 (x+3)=log 3... (answered by jsmallt9)
What is the first step in solving this logarithmic equation: log 3 + log (x + 1) = log... (answered by ewatrrr)
solve the following logarithmic equation log(3x+7)=1+log(x-6) can someone please... (answered by Fombitz)
Solve the logarithmic equation.reject any value of x that is not in the domain of the... (answered by josgarithmetic)