If $$\log 2 = 0.30103,$$ the number of digits in $${4^{50}}$$ is -
A. 30
B. 31
C. 100
D. 200
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \log {4^{50}} \cr & = 50\log 4 \cr & = 50\log {2^2} \cr & = \left( {50 \times 2} \right)\log 2 \cr & = 100 \times \log 2 \cr & = \left( {100 \times 0.30103} \right) \cr & = 30.103 \cr & \therefore {\text{characteristic}} = 30, \cr} $$Hence, the number of digits in $${{\text{4}}^{50}} = 31$$
Related Questions on Logarithm
Which of the following statements is not correct?
A. log10 10 = 1
B. log (2 + 3) = log (2 x 3)
C. log10 1 = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3
$${{\log \sqrt 8 } \over {\log 8}}$$ is equal to:
A. $$\frac{1}{6}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{1}{8}$$
Join The Discussion