Express the value of the inverse hyperbolic function in terms of natural logarithms.
-$\tanh ^ { - 1 } \left( \frac { 9 } { 10 } \right)$
A) $\frac { 1 } { 2 } \ln 209$
B) $\frac { 1 } { 2 } \ln 1$
C) $\frac { 1 } { 2 } \ln - 19$
D) $\frac { 1 } { 2 } \ln 19$

Question

Quizplus · Accepted Answer

We know that $	anh^{-1}(x) = \frac{1}{2} \ln \frac{1+x}{1-x}$. So, we have 
\begin{align*}
	anh^{-1}\left(\frac{9}{10}ight) &= \frac{1}{2} \ln \frac{1+\frac{9}{10}}{1-\frac{9}{10}} \
&= \frac{1}{2} \ln \frac{19}{1} \
&= \frac{1}{2} \ln 19
\end{align*}
Therefore, the answer is choice D, $\frac{1}{2} \ln 19$.

Express the Value of the Inverse Hyperbolic Function in Terms tanh⁡−1(910)\tanh ^ { - 1 } \left( \frac { 9 } { 10 } \right)tanh−1(109​)

Express the Value of the Inverse Hyperbolic Function in Terms $\tanh ^ { - 1 } \left( \frac { 9 } { 10 } \right)$