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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?

 Mar 19, 2021

Best Answer 

 #2
avatar+956 
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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.

 Mar 20, 2021
 #1
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2^0, 2^1, 2^2, ..., 2^9 -> 10 numbers

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

 

Total of 17 numbers

 Mar 20, 2021
 #2
avatar+956 
+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

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