log3(x-1)=log9(x+5)怎么解?

题目

log3(x-1)=log9(x+5)怎么解?
RT,3和9是底数..

答案

log9(x+5)=log(3)^2(x+5)=1/2log3(x+5)=log3√(x+5)
log3(x-1)=log3√(x+5)
x-1=√(x+5)
x^2-2x+1=x+5
x^2-3x-4=0
(x-4)(x+1)=0
x1=4,x2=-1
经检验得x2=-1不符合,舍去
x=4