Can someone please help me out?? I'm starting to confuse myself.

log(x-1) = 2 - log (x+1)

okay so heres what i did:

added log (x+1) to the other side, hence log (x-1) + log (x+1) = 2

then i used product rule . . .log (x-1)(x+1) = 2

now i end up getting (x+1)(x-1) = 100 after getting rid of the log with base 10, and 10^2.

x^2 = 101

idk this just seems wrong and it is probably, so if anyone can help me out i'd appreciate that a lot. thanks.