Evaluate natural log of 1/( square root of e^7)

Problem

ln(1/√(,e^7))

Solution

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

√(,e^7)=e^(7/2)

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

1/(e^(7/2))=e^(−7/2)

3. Substitute this back into the natural logarithm expression.

ln(e^(−7/2))

4. Use the logarithm power rule ln(e^x)=x to simplify the expression.

−7/2

Final Answer

ln(1/√(,e^7))=−7/2

Want more problems? Check here!