are (x1​,y1​) and (x2​,y2​). Find log30​(x1​y1​x2​y2​).
Solution:
Let p=log225​x=1/logx​225 and q=log64​y=1/logy​64. 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 x1​x2​=225p1​225p2​=225p1​+p2​=2256,y1​y2​=64q1​+q2​=642, and log30​(x1​y1​x2​y2​)=log30​(2256642)=log30​(1512212)=log30​3012=12​.