Find the Domain log of 2x = log of 31

Problem

(log_)(2*x)=(log_)(31)

Solution

1. Identify the logarithmic expression in the equation, which is (log_)(2*x)

2. Recall the definition of the domain for a logarithmic function (log_)(u) which requires the argument u to be strictly greater than zero.

3. Set up the inequality for the argument of the logarithm on the left side of the equation.

2*x>0

4. Solve the inequality for x by dividing both sides by 2

x>0

5. Express the domain in interval notation based on the inequality.

(0,∞)

Final Answer

Domain: *(0,∞)

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