Question

设 x,y,z是正实数,且3的 x次方=4的y次方=6的z次方

Answer 1

(1)因为3^x=4^y=6^z,所以lg3^x=lg4^y=lg6^z,即xlg3=ylg4=zlg6,令xlg3=ylg4=zlg6=k,x=k/lg3,y=k/lg4,z=k/lg6,则左边=1/z-1/x=lg6/k-lg3/k=lg2/k,右边=1/2y=lg4/2k=2lg2/2k=lg2/k,所以左边=右边.(2)同样,3x=3k/lg3,4y=...