Question

Help pls!!

Answer 1

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

mark me as a brill please