Question

How many times do you have to square `2` for it to become a multiple of `3`? Is it possible? In algebraic terms, `2^x =3y`.

Answer 1

Not only is it possible to satisfy `2^x=3y` but there are two sets of Real points where it happens. See the graph below. However, if we restrict `y` to being a positive integer, then there is no value of `x` that will work.

Explanation:

We can graph the two expressions and see where they intersect. And they do intersect twice and so there are 2 sets of `(x,y)` that will satisfy the equation `2^x=3y`

graph{(y-2^x)(y-3x)=0[0,5,-5,15]}

However, usually we restrict discussions of multiples to positive integers (and so 3, 6, 9, 12, and so on are multiples of 3) and there is no value of `x` that will result in a multiple of 3.