若lg2=a,lg3=b,则以5为底12的对数=?

lg2=ln2/ln10=ln2/(ln2+ln5)=a
倒数一下得 1+ln5/1n2=1/a
ln5/1n2=1/a-1
ln2/ln5=a/(1-a)
lg3=ln3/ln10=ln3/(ln2+ln5)=b
ln3=b(ln2+ln5)
log5 12=ln12/ln5=(ln3+ln4)/ln5=ln3/ln5+2ln2/ln5
=b(ln2+ln5)/ln5+2a/(1-a)
=bln2/ln5+b+2a/(1-a)
=ab/(1-a)+b+2a/(1-a)
=(2a+b)/(1-a)