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 $\ln \frac{1}{x} = -\ln x$. Therefore, we have $\ln \frac { 1 } { \sqrt [ 2 ] { e } } = \ln e^{-\frac{1}{2}}= -\frac{1}{2} \ln e = -\frac{1}{2}$. Choice C is the only answer option that matches this value.

Find the Exact Value of the Logarithm Without Using a Calculator