Source: Extra Practice

If log_{10} 2 = 0.3010, the number of digits in 2^{50} is:

Options

Option A

15

Option B is correct

16

Option C

50

Option D

14

Explanation

To find the number of digits in N = 2^{50}, take the common log: log N = log(2^{50}) = 50 * log 2 = 50 * 0.3010 = 15.05. The characteristic is 15. The number of digits in a number is (characteristic + 1). Therefore, digits = 15 + 1 = 16. Option A is just the characteristic.