Question

已知log2 (3)=m,求log12 根号54

Answer 1

log2 (3)=lg3/lg2,log2 (3)=m所以lg3/lg2=m.

log12 根号54=1/2lg(3^3*2)/lg(3*2^2)=1/2(3lg3+lg2)/(lg3+2lg2)

将1/2(3lg3+lg2)/(lg3+2lg2)分子分母同除以lg2得

1/2[3(lg3/lg2)+1]/[(lg3/lg2)+2]

将lg3/lg2=m代入1/2[3(lg3/lg2)+1]/[(lg3/lg2)+2]=1/2[3m+1]/[m+2]=(3m+1)/(2m+4)