Evaluate natural log of natural log of e^(e^200)

Problem

ln(ln(e^(e^200)))

Solution

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

2. Substitute x=e^200 into the property to simplify the inner natural log.

ln(e^(e^200))=e^200

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

ln(e^200)

4. Apply the property ln(e^x)=x again, this time with x=200

ln(e^200)=200

Final Answer

ln(ln(e^(e^200)))=200

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