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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 expo

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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

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Can you edit it and write it properly please.

Mar 25, 2019
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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
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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.

Apr 2, 2019
edited by Melody  Apr 2, 2019