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

 Mar 25, 2019
 #1
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Can you edit it and write it properly please.

 Mar 25, 2019
 #2
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Revised Question: 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?

 Apr 2, 2019
 #3
avatar+100008 
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Revised Question: 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?

 

2^9 = 512    So that is  9+9+1 = 19 powers of 2

3^6=729     so that is 6+6+1 = 13 powers of 3

 

Now you just have to work out how many are powers of 2 and 3 because they have  been counted twice.

 

If they are powers of 2 and 3 that means they are powers of 6

6^3 = 216 which is the biggest so that is  3+1+3 = 9

 

So I think the answer is      19+13-9 = 23

 

 

It is a petty you are a guest and not a member as that means you will probably never realize this question has been answered. sad

 Apr 2, 2019
edited by Melody  Apr 2, 2019

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