Find the domain of the logarithmic function. f(x) = ln (8 - x)

Question

Show all work, step by step. 

Answer 1

To find the domain of f(x) = ln(8 - x), I need to determine when the argument of the logarithm is positive.

Requirement: The argument of a natural logarithm must be positive.

So I need: 8 - x > 0

Solving the inequality:

8 - x > 0

8 > x

x < 8

Domain: x < 8 or in interval notation: (-∞, 8)

The function is defined for all real numbers less than 8.

Answer 2

f(x) = ln (8 - x)

Domain = {x l (8-x) > 0}

 

8 - x > 0

 

-x > -8

 

x < 8

Therefore, Domain: {x l x < 8 }

Domain: (-∞,8)