Question

If xy = yx and x = 2y, the value of y is:

Answer 1

Answer:

2

Step-by-step explanation:

xy=yx  and x=2y

So we can substitute and say that:

(2y)y=y2y

So simplifying:

2yyy=yyyy

Divide through by yy since it cannot be 0:

2y=yy

Then, take logs on both sides (I'll use base e):

yln2=ylny

Again, as y≠0 since 00 is undefined, we can divide by y. We can also undo the logs after by raising both sides to the power of e:

ln2=lny2=y

Thus the only solution is y=2, x=4.