Question

6的X次方加2乘4的X次方=9的X次方 怎么算

Answer 1

两边同除以6^x,

1+2*2^x/3^x=(3/2)^x,

1+2*(2/3)^x=(2/3)^(-x),

设(2/3)^x=t,

1+2t=1/t,

2t^2+t-1=0,

(2t-1)(t+1)=0,

t=1/2,或t=-1(不合题意,舍去）,

(2/3)^x=1/2,

两边取常用对数,

lg(2/3)^x=lg(1/2),

x(lg2-lg3)=-lg2,

∴x=lg2/(lg3-lg2).