I would like to know how do I calculate following number:
How many times do I need to divide a specific number to get a number that is one point something ( 1.xxx ).
Example for better understanding:
$10 / 2 = 5$ ($n=1$)
$5 / 2 = 2.5$ ($n=2$)
$2.5 / 2 = $1.25 ($n=3$)
In this case, the answer would be $n=3$. But how do I calculate it let's say for $120000$?
Many thanks to all in advance.
George
Let $K$ be the number ($K>1$) that you want to divide. Say that you have to divide it $n$ times. Then $$1\le K/2^n<2$$ Therefore $$0=\log_2 1\le -n+\log_2 K<\log_2 2=1$$ $$n\le\log_2 K<n+1$$ $$n=\lfloor \log_2 K\rfloor$$