Question 441483
Log(x+2)=-log(x-1)+1
Log(x+2)+log(x-1) = 1
Log(x+2)(x-1) = 1
(x+2)(x-1) = 10^1
x^2+x-2 = 10
x^2+x-12 = 0
(x+4)(x-3) = 0
x = {-4,3}
You can toss out the -4 (extraneous solution) leaving:
x = 3