11/04/2025
2025年 中學文憑試 Q34
其實教科書都冇提過，當然唔知 exp and log function 有呢d相交點。睇呢份paper 就清楚哂 (*試過用deepseek 都答得一半半, 冇提3個相交點，問深入就 server busy)
a^x=loga(x)
當a於0至1之問，交點數目是1或3. [參考 x=e^(-e)] (x=0.066)
(0,0.066) => 3
(0.066,1) => 1
the number of possible intersections is 1 or 3 where a is between 0 and 1.
當a大於1,交點目是0,1,2 [參考e^(1/e)](x=1.445)
(1,1.445) => 2
x=1.445 => 1
(1.445, +inf) => 0
the number of possible intersections is 0,1 or 2 where a is larger than 1.
參考以下：
https://ami.uni-eszterhazy.hu/uploads/papers/finalpdf/AMI_43_from159to170.pdf
