Evaluate e^(-2 natural log of 2)

Problem

e(−2*ln(2))

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 a*ln(b)=ln(ba) to the exponent.

e(−2*ln(2))=eln(2(−2))

3. Simplify the exponent by calculating the value of the power.

2(−2)=1/2=1/4

4. Substitute the simplified value back into the expression.

eln(1/4)

5. Apply the inverse property of logarithms and exponentials, eln(x)=x to find the final value.

eln(1/4)=1/4

Final Answer

e(−2*ln(2))=1/4

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