Given that $a , b , c$ are real numbers satisfying $1 < a < 10$, $b = \log a$, $c = \log b$, select the correct option. (1) $c < 0 < b < 1$ (2) $0 < c < 1 < b$ (3) $0 < c < b < 1$ (4) $1 < c < b$ (5) $c < b < 0$
Given that $a , b , c$ are real numbers satisfying $1 < a < 10$, $b = \log a$, $c = \log b$, select the correct option.\\
(1) $c < 0 < b < 1$\\
(2) $0 < c < 1 < b$\\
(3) $0 < c < b < 1$\\
(4) $1 < c < b$\\
(5) $c < b < 0$