已知log2 (3)=m,求log12 根号54

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 23:05:28

已知log2 (3)=m,求log12 根号54
已知log2 (3)=m,求log12 根号54

已知log2 (3)=m,求log12 根号54
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)

解:log12(sqrt(54))=log12(sqrt(2*3^3))=1/2log12(2)+3/2log12(3)=1/2/log2(12)+3/2/log3(12)=1/2/(2+log2(3))+3/2/(1+2log3(2))=
1/2/(2+m)+3/2/(1+2/m)=(1+3m)/(4+2m)