Find the Domain log of 4x+2- log of 3=1

Problem

(log_)(4*x+2)−(log_)(3)=1

Solution

1. Identify the condition for the logarithm to be defined. The argument of any logarithmic function must be strictly greater than zero.

2. Set up the inequality for the expression inside the first logarithm.

Argument>0

4*x+2>0

3. Solve the inequality for x to find the restriction on the domain.

4*x>−2

x>−2/4

x>−1/2

4. Check the other terms in the equation. The term (log_)(3) is a constant and is defined for all x because 3>0

5. Express the domain in interval notation based on the inequality x>−0.5

Final Answer

Domain=(−1/2,∞)

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