Question 1
SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
Let $x,y$ be real numbers with $x>1$ and $y>1$. Find the smallest value of $$\frac{\log_x2011+\log_y2011}{\log_{xy}2011}.$$
Let $x,y$ be real numbers with $x>1$ and $y>1$. Find the smallest value of $$\frac{\log_x2011+\log_y2011}{\log_{xy}2011}.$$