已知log2(5)=m ,log5(3)=n,求用m,n表示lg180

m=log2(5)=lg5/lg2=lg(10/2)/lg2=(1-lg2)/lg2
(m+1)lg2=1
lg2=1/(m+1)
lg5=1-lg2=1- 1/(m+1)=m/(m+1)
n=log5(3)=lg3/lg5
lg3=nlg5=mn/(m+1)
lg180=lg(10×2×3²)
=lg10+lg2+2lg3
=1+ 1/(m+1) +2mn/(m+1)
=1 +(2mn+1)/(m+1)