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(b^a)

e^ln((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.

e^ln(9/8)

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

9/8

Final Answer

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

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