If $$\log 2 = 0.30103,$$    the number of digits in $${4^{50}}$$ is -

$$\eqalign{ & \log {4^{50}} \cr & = 50\log 4 \cr & = 50\log {2^2} \cr & = \left( {50 \times 2} \right)\log 2 \cr & = 100 \times \log 2 \cr & = \left( {100 \times 0.30103} \right) \cr & = 30.103 \cr & \therefore {\text{characteristic}} = 30, \cr} $$
Hence, the number of digits in $${{\text{4}}^{50}} = 31$$