Question 77282
*[Tex \large \log_{(x-1)}{9}=2] This expression is equivalent to:


*[Tex \large (x-1)^2=9]

*[Tex \large sqrt{(x-1)^2}=sqrt{9}] Take the square root of both sides

*[Tex \large x-1=\pm 3]

Which means 

*[Tex \large x-1=3] <u>or</u> *[Tex \large x-1=-3]


*[Tex \large x-1+1=3+1] <u>or</u> *[Tex \large x-1+1=-3+1] Add 1 to both sides for each case

So

*[Tex \large x=4] <u>or</u> *[Tex \large x=-2]

<p>
Check:

*[Tex \large (4-1)^2=9] Plug in x=4

*[Tex \large (3)^2=9]

*[Tex \large 9=9] works


*[Tex \large ((-2)-1)^2=9] Plug in x=-2

*[Tex \large (-3)^2=9]

*[Tex \large 9=9] works