Express the value of the inverse hyperbolic function in terms of natural logarithms.
-$\cosh ^ { - 1 } 7$
A) $\ln ( 7 + \sqrt { 48 } )$
B) $\ln ( 7 + \sqrt { 50 } )$
C) $\ln ( 14 )$
D) $\ln ( 7 - \sqrt { 48 } )$

Question

Quizplus · Accepted Answer

We use the formula $\cosh ^ { - 1 } x = \ln ( x + \sqrt { x ^ { 2 } - 1 } )$. Plugging in $x = 7$, we get:
$$\cosh ^ { - 1 } 7 = \ln ( 7 + \sqrt { 7 ^ { 2 } - 1 } ) = \ln ( 7 + \sqrt { 48 } )$$
Therefore, the correct choice is A.

Express the Value of the Inverse Hyperbolic Function in Terms cosh⁡−17\cosh ^ { - 1 } 7cosh−17

Express the Value of the Inverse Hyperbolic Function in Terms $\cosh ^ { - 1 } 7$