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?

Guest Mar 19, 2021

#2**+2 **

from 1 to 1000:

2^0, 2^1, ..., 2^9 (10 numbers)

3^0, 3^1, ..., 3^6 (7 numbers)

2^0 = 3^0 = 1 was counted twice, so 16 numbers from 1 to 1000

from 1/1000 to 1:

1/2^9, 1/2^8, ..., 1/2 (9 numbers)

1/3^6, 1/3^5, ..., 1/3 (6 numbers)

Therre are 15 numbers from 1/1000 to 1.

Overall, there are **31** numbers.

CubeyThePenguin Mar 20, 2021

#1**0 **

2^0, 2^1, 2^2, ..., 2^9 -> 10 numbers

3^0, 3^1, 3^2, ..., 3^6 -> 7 numbers

Total of 17 numbers

Guest Mar 20, 2021

#2**+2 **

Best Answer

from 1 to 1000:

2^0, 2^1, ..., 2^9 (10 numbers)

3^0, 3^1, ..., 3^6 (7 numbers)

2^0 = 3^0 = 1 was counted twice, so 16 numbers from 1 to 1000

from 1/1000 to 1:

1/2^9, 1/2^8, ..., 1/2 (9 numbers)

1/3^6, 1/3^5, ..., 1/3 (6 numbers)

Therre are 15 numbers from 1/1000 to 1.

Overall, there are **31** numbers.

CubeyThePenguin Mar 20, 2021