Question

已知log以18为底9的对数＝a,18的次方＝5,用含a,b的式子表示log以36为底5为对数

Answer 1

由已知,有

a=log18(9)=log2(9)/log2(18)=2log2(3)/[1+2log2(3)]

b=log18(5)=log2(5)/log2(18)=log2(5)/[1+2log2(3)]

由此解得 log2(3)=a/[2(1-a)],log2(5)=b/(1-a),

所以,根据对数换底公式得

log36(5)=log2(5)/log2(36)=log2(5)/[2+2log2(3)]=b/(2+a).