Evaluate natural log of 1/(e^(5x))

Problem

ln(1/(e(5*x)))

Solution

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

1/(e(5*x))=e(−5*x)

2. Substitute the simplified expression back into the natural logarithm.

ln(e(−5*x))

3. Apply the inverse property of logarithms, which states that ln(eu)=u for any real number u

−5*x

Final Answer

ln(1/(e(5*x)))=−5*x

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