Evaluate e^(2 natural log of 8)

Problem

e(2*ln(8))

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

2*ln(8)=ln(8)

3. Simplify the term inside the logarithm by calculating the square of 8

8=64

4. Substitute the simplified exponent back into the original expression.

eln(64)

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

eln(64)=64

Final Answer

e(2*ln(8))=64

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