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? Hint: Remember that we're counting all possible numbers, not just integers.
The possible numbers are 2^0, 2^1, ..., 2^9 and 3^0, 3^1, .., 3^6. Total number of powers = 10 + 7 = 17.
Um... sorry but that's false, I feel like its close though, and ill base my solution off of that :)
2^-9, 2^-8, 2^-7, 2^-6, 2^-5, 2^-4, 2^-3, 2^-2, 2^-1, 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^8, 2^9
3^-6, 3^-5, 3^-4, 3^-3, 3^-2, 3^-1, 3^0, 3^1, 3^2, 3^3, 3^4, 3^5, 3^6
I count a total of 32.
