Evaluate e^(-2 natural log of 5)

Problem

e(−2*ln(5))

Solution

1. Identify the expression as a base e raised to a power involving a natural logarithm.

2. Apply the power rule of logarithms, which states n*ln(a)=ln(an) to the exponent.

e(−2*ln(5))=eln(5(−2))

3. Use the inverse property of logarithms and exponentials, eln(x)=x to simplify the expression.

eln(5(−2))=5(−2)

4. Evaluate the negative exponent by rewriting it as a reciprocal.

5(−2)=1/5

5. Simplify the denominator by calculating the square of 5.

1/5=1/25

Final Answer

e(−2*ln(5))=1/25

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