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?

Guest Mar 25, 2019

#2**0 **

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?

Guest Apr 2, 2019

#3**+1 **

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.

Melody Apr 2, 2019