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