Question

解方程 log9(x)-3logx^2(3)=1

Answer 1

运用换底公式,变成以3为底的对数.

log3(x)/log3(9)-3*log3(3)/log3(x^2)=1

log3(x) /2- 3/2log3(x) =1

[log3(x)]^2 -3 =2log3(x)

令a=log3(x)

a^2-3=2a a^2-2a-3=0

a=-1 or a=3

log3(x)=-1 或 3

x=3^(-1)=1/3 或x=3^3=27.