The Domain of natural log

Question

How would I go about getting the domain of this function and expressing it in interval notation:

f(x)=[ln(x^5-4)]^3

Answer 1

Hello Dwayn,

The function whose domain you're trying to find is [ln(x^5-4)]^3

Typically, to find the domain of logarithmic functions, you want to make sure the thing you're taking the log of is strictly greater than zero. In this case, you're taking the (natural) log of x^5 - 4. Therefore, you need to set x^5 -4 > 0 and solve for it.

Adding 4 on both sides, you get: x^5 > 4

Take the fifth roof of both sides and you get: x > ⁵√4 (I couldn't write it otherwise, but it's the fifth root of 4)

In interval notation, that translates to (⁵√4,∞) as the domain of f(x)