Question

find domain of log
f(x)=ln(5 - x)

Explanation:

Step1: Recall domain of natural log

The natural logarithm function \( \ln(u) \) is defined when \( u > 0 \).

Step2: Apply to given function

For \( f(x)=\ln(5 - x) \), set the argument \( 5 - x > 0 \).

Step3: Solve the inequality

Subtract 5 from both sides: \( -x > -5 \). Multiply both sides by -1 (reverse inequality): \( x < 5 \).

Answer:

The domain of \( f(x)=\ln(5 - x) \) is all real numbers \( x \) such that \( x < 5 \), or in interval notation \( (-\infty, 5) \).