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

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.