Question

若 log以a为底x的对数=2,log以b为底x的对数=3,log以c为底x的对数=6,则log以abc为底x的对数的值

Answer 1

由loga(b)=1/logb(a)

又loga(x)=2,logb(x)=3,logc(x)=6,

∴logx(a)=1/2,logx(b)=1/3,logx(c)=1/6

logabc(x)

=1/logx(abc)

=1/[logx(a)+logx(b)+logx(c)]

=1/(1/2+1/3+1/6)

=1