Let $a=30 !, b=50!,$ and $c=100!.$ Consider the following numbers:
$$\log _a c, \quad \log _c a, \quad \log _b a, \quad \log _a b$$
Which one of the following inequalities is $\text{CORRECT?}$
- $\log _c a<\log _b a<\log _a b<\log _a c$
- $\log _c a<\log _a b<\log _b a<\log _b c$
- $\log _c a<\log _b a<\log _a c<\log _a b$
- $\log _b a<\log _c a<\log _a b<\log _a c$