Find the Value of the Expression $\log _ { b } A = 4$

Multiple Choice

Find the value of the expression.
-Let $\log _ { b } A = 4$ and $\log _ { b } B = - 5$ . Find $\log _ { b } 2 \sqrt { A B }$ .

A) $- 0.500$
B) $- 4.472$
C) $4.472$
D) $2 \sqrt { - 20 }$