sorry for my english and sorry if it's not the right forum
i'm asked to say the amount of numbers of 2^56, and I don't know how!
thank u!!
do you mean the number of digits?
if so we want to find an integer x so that 10^(x) < 2^56 < 10^(x+1).
taking common logarithms: x < log(2^56) < x+1
x < 56(log(2)) < x+1
log(2) is approx. 0.301, so 56(0.301) = 16.856....therefore 2^56 has 17 digits.
(10^x has x+1 digits, a 1 and x 0's after)
10^x is the smallest number with x+1 digits, and 10^(x+1) is the smallest number with x+2 digits.
for example: 10 is the smallest number with 2 digits (9 has just one digit), and 100 is the smallest number with 3 digits (99 has only 2).
so if a number has 2 digits, it lies between 10 and 100.