Evaluate e^(1/2* natural log of 81/64)

Problem

e(1/2*ln(81/64))

Solution

1. Apply the power property of logarithms to the exponent, which states that a*ln(b)=ln(ba)

eln((81/64)(1/2))

2. Simplify the exponent by calculating the square root of the fraction.

(81/64)(1/2)=√(,81)/√(,64)

√(,81)/√(,64)=9/8

3. Substitute the simplified value back into the logarithmic expression.

eln(9/8)

4. Apply the inverse property of natural logarithms and exponentials, where eln(x)=x

9/8

Final Answer

e(1/2*ln(81/64))=9/8

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