log(a)ab=1/p,则log(ab)a/b打括号的是底数已知lg2=0.301,lg3=0.4771,求lg12,lg9/2,lg3.6,lg根号6/2

Question

log(a)ab=1/p,则log(ab)a/b打括号的是底数
已知lg2=0.301,lg3=0.4771,求lg12,lg9/2,lg3.6,lg根号6/2

Answer 1

1.log(a)ab=1/p,Log(a)a+Log(a)b=1/p,1+Log(a)b=1/p
Log(a)b=(1-p)/p
log(ab)a/b(换底)=[Log(a)a/b]/Log(a)ab
=[Log(a)a-Log(a)b]/(1/p)=[1-(1-p)/p]/(1/p)=
=p-(1-p)
=2p
2.已知lg2=0.301,lg3=0.4771,求lg12,lg9/2,lg3.6,lg根号6/2
(1)lg12=Lg(2×2×3)=2Lg2+Lg3=1.0791
(2)lg9/2=Lg9-Lg2=2Lg3-Lg2=0.4532
(3)lg3.6=Lg(36/10)=Lg36-Lg10
=Lg(2^2×3^2)-1
=2(Lg2+Lg3)-1
=1.5562
(4)lg根号6/2=1/2Lg6/2=1/4Lg6=1/4(Lg2+Lg3)
=0.3891