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

Problem

ln(1/√(,e7))

Solution

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

√(,e7)=e(7/2)

2. Apply the negative exponent rule 1/(xa)=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(ex)=x to simplify the expression.

−7/2

Final Answer

ln(1/√(,e7))=−7/2

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