How do i solve for x? log (x-2) = -1 + log (x+1)

For this question you can say:
log(x-2) - log(x+1) = -1 
and you should know that log(x-2) minus log(x+1) is equal to:
log((x-2)/(x+1)) 
so now you have:
log((x-2)/(x+1)) = -1 
now you can say:
(x-2)/(x+1) = 10^ -1 or (x-2)/(x+1) = 1/10 
now you can say:
10(x-2) = x+1 
10x -20 = x +1 
10x - x = 20+1 
9x = 21 
x = 21/9 
x = 7/3 :)))
I hope this is helpful
have a nice day