Question

If log2=0.301 then find the number of digits in 2¹⁰²⁴.

Answer 1

if you put logarithm to 2^1024 ,you can get the number of digits. 1024log(2)=1024(0.301)=308.224 when it comes in decimals round it off to next number 309. hence no of digits in2^1024 is 309.

Answer 2

Let x = (2)^1024.

Apply log on both sides, we get

= > log x = log(2)^1024

= > log x = 1024 log 2

= > log x = 1024 * 0.301

= > log x = 308.22

The characteristic of x = 308.

Hence, the number of digits in 2^1024 = 308 + 1

= 309.

Therefore, we can conclude that 2^1024 consists of 309 digits.

Hope this helps!