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

Problem

ƒ(x)=ln(x−3)

Solution

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

x−3>0

2. Solve the inequality for x to find the domain.

x>3

3. Express the domain in interval notation.

Domain:(3,∞)

4. Analyze the behavior of the natural log function to determine the range. The natural logarithm function ln(u) outputs all real values as u varies from 0 to ∞

Range:(−∞,∞)

Final Answer

Domain:(3,∞),Range:(−∞,∞)

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