Find the Domain f(x) = natural log of x-6

Problem

ƒ(x)=ln(x−6)

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−6>0

3. Solve the inequality for x by adding 6 to both sides.

x>6

4. Express the domain in interval notation. Since x must be strictly greater than 6 the interval starts at 6 with a parenthesis and goes to infinity.

(6,∞)

Final Answer

Domain:(6,∞)

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