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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.

 Mar 13, 2021
 #1
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The possible numbers are 2^0, 2^1, ..., 2^9 and 3^0, 3^1, .., 3^6.  Total number of powers = 10 + 7 = 17.

 Mar 13, 2021
 #2
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Um... sorry but that's false, I feel like its close though, and ill base my solution off of that :)

Guest Mar 13, 2021
 #3
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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.

 Mar 14, 2021

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