If $a,bc \neq 0$ and belong to the set $\{0,1,2,3.......,9\},$ then $\log _{10} \bigg(\large \frac{a+10 b +10^2 c}{10^{-4} a +10^{-3}b +10^{-2} c}\bigg)$ is equal to :

Question

$$\begin {array} {1 1} (a)\;1 & \quad (b)\;2 \\ (c)\;3 & \quad (d)\;4 \end {array}$$