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The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$   when expressed in usual form, is -

A. 16

B. 17

C. 18

D. 19

Answer: Option C

Solution(By Examveda Team)

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

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