Evaluate natural log of 1/( square root of e^3)

Problem

ln(1/√(,e3))

Solution

1. Rewrite the square root as a fractional exponent using the rule √(,xn)=x(n/2)

√(,e3)=e(3/2)

2. Apply the negative exponent rule 1/(xn)=x(−n) to move the expression to the numerator.

1/(e(3/2))=e(−3/2)

3. Substitute this back into the natural logarithm expression.

ln(e(−3/2))

4. Use the logarithm property ln(ex)=x to simplify the expression.

−3/2

Final Answer

ln(1/√(,e3))=−3/2

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