Find the Domain f(x)=3 natural log of x-1

Problem

ƒ(x)=3*ln(x−1)

Solution

1. Identify the restriction for the natural logarithm function. The argument of a logarithm must be strictly greater than zero.

2. Set up the inequality by taking the expression inside the natural log and making it greater than zero.

x−1>0

3. Solve the inequality for x by adding 1 to both sides.

x>1

4. Express the domain in interval notation. Since x must be greater than 1 but not equal to 1 the interval starts at 1 with a parenthesis.

(1,∞)

Final Answer

Domain:(1,∞)

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