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
May 29, 2017
Answer:
There is no integer
Explanation:
In a similar way to classifying numbers as odd or even, we can classify numbers as one of the following:

A multiple of
#3# . That is of form#3k# 
One more than a multiple of
#3# . That is of form#3k+1# 
Two more than a multiple of
#3# . That is of form#3k+2#
If we multiply a number of the form
#2(3k+1) = 3(2k)+2#
If we multiply a number of the form
#2(3k+2) = 6k+4 = 6k+3+1 = 3(2k+1)+1#
Hence we find that successive powers of
#2^0 = 1 = 3(0)+1#
#2^1 = 2 = 3(0)+2#
#2^2 = 4 = 3(1)+1#
#2^3 = 8 = 3(2)+2#
etc.