1.方程式(log2x)(log3x)=30兩根之積為 2.3的x次方=2的y次方=144,則(x-2)(y-4)=?

設兩根為p,q
Set t=logx
(log2+t)(log3+t)=30
t^2+(log2+log3)t+log2log3=30
兩根為logp,logq
logp+logq=－(log2+log3)=－log6=log(1/6)
pq=1/6
2.3^x=2^y=144,則(x－2)(y－4)=?
Sol
3^x=144
3^(x－2)=144/9=16
(x－2)log3=log16
2^y=144
2^(y－4)=144/16=9
(y－4)log2=log3
(x－2)(y－4)
=(log16/log3)*((log9/log2)
=(4log2/log3)*(2log3/log2)
=8