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How many different rational 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 a (possibly negative) integer?

 Jan 7, 2019
 #1
avatar+99331 
+1

Why don't you just count them?

 

2^10=1024 that is too big  so  1/2^10 is too little

2^9 = 512  that is the biggest power of 2 and 2^-9 is the smallest   So that is 9+9+1=19     

(9 negative, nine positive  the one extra one is 2^0=3^0=1)

 

Now do the same for powers of 3  

 

and find the total :)

If you want more help then ask. But show me what you have tried. :)

 Jan 7, 2019
 #2
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+1

I got 32. Does that seem right?

Guest Jan 7, 2019
 #3
avatar+99331 
+1

I got 32. Does that seem right?

 

It is nice to hear from you  laugh

 

Lets see.

I already got 19 for the twos

32-19=13

Mmm that does not look good. It should be an even number.

maybe you counted 1 twice?

 

Lets see.

 

3^6 = 729   the next one will be bigger than 1000.

 

So I think the answer is   19+12= 31

 

You counted 1 twice  wink

Melody  Jan 8, 2019

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