Question

If x>1,y>1 , then the minimum value of logxy + logyx is

Answer 1

Answer:

Correct option is

A

9

We have logyx+logxy=2,x2+y=12

If logyx=a , then logxy=a1,[∵logab=logba1] 

⇒a+a1=2

⇒a2+1=2a

⇒(a−1)2=0

⇒a=1

Hence, y=x

Substituting in the equation, we get 

x2+x−12=0

Hence, x=3 or x=−4 

Since x is a base in the logarithmic function, x has to be positive. 

Hence, x=3 and y=3

Therefore, xy=9