Evaluate natural log of natural log of e^(e^400)

Problem

ln(ln(e^(e^400)))

Solution

1. Identify the innermost expression, which is e^(e^400)

2. Apply the property of natural logarithms ln(e^x)=x to the first layer of the expression.

3. Simplify the inner logarithm:

ln(e^(e^400))=e^400

4. Substitute this result back into the outer natural logarithm:

ln(e^400)

5. Apply the property ln(e^x)=x again to the remaining expression.

6. Simplify the final result:

ln(e^400)=400

Final Answer

ln(ln(e^(e^400)))=400

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