What is the least integer n such that 1/(2^n)

Question

What is the least integer n such that 1/(2^n) < 0.001

Answer options:
10
11
500
501
There is no such least integer

On the GRE you can only use a very basic calculator that has no "power" button.  How can I solve this without a fancy calculator?

anonymous · Answer

Out of those answers, the first one, 10, would be it.
Without a fancy calculator, just do the math in your head. 2^n is simply doubling numbers.
2^0 = 1
2^1= 2
so just continue on... 2,4,8,16,32,64,128,256,512,1024

So it's 1/1024, which 1/1000 would be 0.001, so 1/1024 should be slight less. Perfect!

anonymous · Answer

$$
\frac 1{2^n} < \frac 1{1000}\
2^n > 10^3\
n \ln(2) > 3 \ln(10)\
n >\frac{ 3 \ln(10)}{\ln(2)}=9.96578\
n=10
$$