Evaluate natural log of natural log of x

Problem

ln(ln(x))

Solution

1. Identify the expression as the natural logarithm of the natural logarithm of x

2. Recognize that the task "Evaluate" for a single expression like ln(ln(x)) typically refers to identifying its domain or simplifying it if possible.

3. Determine the domain by noting that the inner function ln(x) must be defined, requiring x>0

4. Apply the condition for the outer function, which requires its argument ln(x) to be strictly positive, meaning ln(x)>0

5. Solve the inequality ln(x)>0 by exponentiating both sides, which results in x>e0 or x>1

Final Answer

ln(ln(x))=ln(ln(x))

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