are (x1,y1) and (x2,y2). Find log30(x1y1x2y2).
Solution:
Let p=log225x=1/logx225 and q=log64y=1/logy64. The given equations then take the form p+q=4 and p1−q1=1, whose solutions are (p1,q1)=(3+5,1−5) and (p2,q2)=(3−5,1+5). Thus x1x2=225p1225p2=225p1+p2=2256,y1y2=64q1+q2=642, and log30(x1y1x2y2)=log30(2256642)=log30(1512212)=log303012=12.