If x, y are two positive real number and x13=y14, then which of the following relations is true?

Taking the LCM of 3 and 4, we get 12. Then, raising both sides of the given equation to the power of 12, we get:

(x^13)^12 = (y^14)^12

x^(1312) = y^(1412)

x^156 = y^168

Dividing both sides by y^12, we get:

(x^156) / (y^12) = y^(168-12) / (y^12)

x^13 = y^14

Therefore, we have shown that (x^4)^5 = (y^3)^5, which simplifies to x^20 = y^15.

So, the given relation x^13 = y^14 implies that x^20 = y^15.