1.

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

Answer»

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!


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