設(shè)數(shù)列{ a(n) }的首項(xiàng)是a(1),a(1)>0,公比是q,q>0,
那么：
a(n)=a(1)·q^(n-1)
lg[a(n)] = lg[a(1)·q^(n-1)] = lg[a(1)]+(n-1)·lg(q)
lg[a(1)] = lg[a(1)]
lg[a(2)] = lg[a(1)]+1·lg(q)
lg[a(3)] = lg[a(1)]+2·lg(q)
……
lg[a(10)] = lg[a(1)]+9·lg(q)
……
A(n) = n·lg[a(1)] + [1+2+……+(n-1)]·lg(q)
= n·lg[a(1)] + [n·(n-1)/2]·lg(q)
= n·{lg[a(1)] + [(n-1)/2]·lg(q)}
于是有：A(19) = 19·{lg[a(1)] + [(19-1)/2]·lg(q)} = 19·lg[a(10)]
同理：B(19) = 19·lg[b(10)]
又：A(19)/B(19) = 19/(2·19+1) = 19/39
即：lg[a(10)]/lg[b(10)] = 19/39
即a(10)的以b(10)為底的對(duì)數(shù) Log[a(10),b(10)] = lg[a(10)]/lg[b(10)] = 19/39
備注：由于這里不方便寫標(biāo)準(zhǔn)的數(shù)學(xué)形式的對(duì)數(shù)表達(dá)式,所以用標(biāo)準(zhǔn)的計(jì)算機(jī)對(duì)數(shù)函數(shù)表達(dá)式Log(number,base)來表示,其中前一個(gè)參數(shù)number表示想要計(jì)算其對(duì)數(shù)的正實(shí)數(shù),后一個(gè)參數(shù)base表示對(duì)數(shù)的底數(shù).