This is pretty simple once you figure out the trick.
All you have to do is make the args common.
Meaning [tex]log_{6}(x + 1) + log_{6}(x) = 1[/tex] is nothing but [tex]log_{6}(x(x + 1)) = 1[/tex]
Which is nothing but: [tex]log_{6}(x^2 + x) = 1[/tex].
Now using the scorpion tail method, this equation can be reframed to being: [tex]6 = x^2 + x[/tex]. You bring 6 to the other side and it'll become: [tex]x^2 + x - 6 = 0[/tex]
Factorise it and you get: [tex](x - 2) * (x + 3)[/tex]
Henceforth, the solution would be [tex]2[/tex] and [tex]-3[/tex]. :D
