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
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 form3k -
One more than a multiple of
3 . That is of form3k+1 -
Two more than a multiple of
3 . That is of form3k+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.