The number of digits in 4^9 × 5^17 , when expressed in usual form, is -

Answer: Option C

$$\begin{array}{rl}& \log \left(4^9\times 5^{17}\right)\\ & =\log \left(4^9\right)+\log \left(5^{17}\right)\\ & =\log {\left(2^2\right)}^9+\log \left(5^{17}\right)\\ & =\log \left(2^{18}\right)+\log \left(5^{17}\right)\\ & =18\log 2+17\log 5\\ & =18\log 2+17\left(\log 10-\log 2\right)\\ & =18\log 2+17\log 10-17\log 2\\ & =\log 2+17\log 10\\ & =0.3010+17\times 1=17.3010\\ & \therefore \text{Characteristic}=17\\ & \text{Hence, the number of digits in }\left(4^9\times 5^{17}\right)=18\end{array}$$