若a,b,c属于R+,且3^a=4^b=6^c,则( ) A.1/c=1/a+1/b B.2/c=2/a+1/b C.1/c=2/a+2/b D.2/c=1/a+2/b
问题描述:
若a,b,c属于R+,且3^a=4^b=6^c,则( ) A.1/c=1/a+1/b B.2/c=2/a+1/b C.1/c=2/a+2/b D.2/c=1/a+2/b
答
答案是B
等式两边取对数:得alg3=2blg2=c(lg2+lg3);整理得1/a=lg3/(2blg2),1/c=(lg2+lg3)/(2blg2)=1/(2b)+lg3/(2blg2)=1/(2b)+1/a,即选项B.