log12(6)=a ,
则由换底公式得 a=log2(6)/log2(12)=log2(6)/[1+log2(6)] ,
因此 log2(6)=a/(1-a) ,
所以 log24(18)=log2(18)/log2(24)
=log2(36/2)/log2(6*4)
=[log2(36)-log2(2)]/[log2(6)+log2(4)]
=[2log2(6)-1]/[log2(6)+2]
=[2a/(1-a)-1]/[a/(1-a)+2]
=[2a-(1-a)]/[a+2(1-a)]
=(3a-1)/(2-a) .