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

Problem

ln(1/√(,e^3))

Solution

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

√(,e^3)=e^(3/2)

2. Apply the negative exponent rule 1/(x^n)=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(e^x)=x to simplify the expression.

−3/2

Final Answer

ln(1/√(,e^3))=−3/2

Want more problems? Check here!