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?

Guest Jan 7, 2019

#1**+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. :)

Melody Jan 7, 2019

#3**+1 **

I got 32. Does that seem right?

It is nice to hear from you

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

Melody
Jan 8, 2019