Find the exact value of the logarithm without using a calculator, if possible. $\ln \frac { 1 } { \sqrt [ 2 ] { e } }$
A) - 2
B) 2
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E) not possible without using a calculator

Question

Quizplus · Accepted Answer

Recall that $\ln\frac{1}{\sqrt{x}}=-\frac{1}{2}\ln{x}$. So we have $\ln\frac{1}{\sqrt[2]{e}}=\ln{e^{-\frac{1}{2}}}=-\frac{1}{2}\ln{e}=-\frac{1}{2}\cdot1=-\frac{1}{2}$. Thus the answer is $\boxed{	extbf{(C) }-\frac{1}{2}}$.

Find the Exact Value of the Logarithm Without Using a Calculator