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.

1 Answer

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.