Question

if log 2= 0.3010 and log 3= 0.4771, find the no of digits in 2 to the power 40​

Answer 1

log 2×20^40

40 log 2

40× 0.3010

Answer 2

Answer:

13 digits

Step-by-step explanation:

The logarithm of a number contains two parts- characteristic and mantissa, which are separated by a decimal point. The characteristic of the logarithm is found by subtracting 1 from the number of digits in the number. So, the number of digits in the number can be found by adding 1 to the characteristic of the logarithm.

Now,

log 2⁴⁰= 40 log 2

= 40× 0.3010

= 12.04.

Here, Characteristic= 12.

Therefore, Number of digits in 2⁴⁰= (12+1)=13.

Hence, there are 13 digits in 2⁴⁰.