Evaluate natural log of 1/(e^4)

Problem

ln(1/(e4))

Solution

1. Rewrite the fraction using negative exponents to simplify the expression inside the logarithm.

1/(e4)=e(−4)

2. Substitute the exponential form back into the natural logarithm.

ln(e(−4))

3. Apply the property of logarithms ln(ex)=x which states that the natural logarithm and the exponential function are inverses.

ln(e(−4))=−4

Final Answer

ln(1/(e4))=−4

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