Problem:
If x,y>0,logy​x+logx​y=310​ and xy=144, then 2x+y​=
Answer Choices:
A. 122​
B. 133​
C. 24
D. 30
E. 36
Solution:
Let v=logy​x. Then, since logx​y=v1​, we solve v+v1​=310​ to find logy​x=v=3 or 31​. Without loss of generality, assume x>y. Then logy​x=3,x=y3 and xy=y4=144 so that y=12​=23​,x=243​ and 2x+y​=2243​+23​​=133​.