# How many numbers has 2 to the 100th?

How many numbers has $2^{100}$?

We put k-as the numbers of the number $2^{100}$, Then we have:$2^{100}=a\cdot&space;10^{k-1}$ where  1<a<10.

By taking the decimal logs in both sides we have:

$100log2=loga+(k-1)$ $\Rightarrow&space;k=1+100log2-loga&space;(0. k  is the whole number 1+100log2. As we know that the  log2=0.30, we find  k=31 numbers.