# 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.

Not only is it possible to satisfy ${2}^{x} = 3 y$ 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.
We can graph the two expressions and see where they intersect. And they do intersect twice and so there are 2 sets of $\left(x , y\right)$ that will satisfy the equation ${2}^{x} = 3 y$
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.