Evaluate natural log of natural log of e^(e^100)

Problem

ln(ln(e(e100)))

Solution

1. Apply the property of natural logarithms ln(ex)=x to the inner expression.

2. Substitute x=e100 into the property to simplify the inner natural log.

ln(e(e100))=e100

3. Rewrite the original expression using the simplified inner term.

ln(e100)

4. Apply the property ln(ex)=x again, this time with x=100

ln(e100)=100

Final Answer

ln(ln(e(e100)))=100

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