Find the Domain

Problem

(log_3)(x+1)+(log_3)(x−1)=(log_3)(2*x)

Solution

1. Identify the constraints for the first logarithmic term. The argument of a logarithm must be strictly greater than zero.

Constraint 1: *x+1>0

x>−1

2. Identify the constraints for the second logarithmic term.

Constraint 2: *x−1>0

x>1

3. Identify the constraints for the logarithmic term on the right side of the equation.

Constraint 3: *2*x>0

x>0

4. Determine the intersection of all identified constraints to find the domain of the equation.

x>−1* and *x>1* and *x>0

⇒x>1

Final Answer

Domain: *(1,∞)

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