Help pls!! 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? Remember that we're counting all possible numbers, not just integers.

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

17 1/3

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4