How many different numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3, where the exponent is an integer?

FUN Q!

look for 1/1000 < x < 1000 where x=2^n, n must be an integer
taking log on the inequalities
log1/1000 < logx < log1000
-3 < logx < 3

take log on x=2^n
logx=log (2^n)=nlog2=0.301n

substituting
-3 < 0.301n < 3
-9.9658 < n < 9.9658
n must be an integer: -9, -8,0, 1,9
ans is 19

u can repeat the same with log(3)