Question

logx + log(x+1) = log 6 . find x

Answer 1

logx + log(x+1) = log6

log[x(x+1)] = log6

x^2 + x = 6

x^2 +x - 6= 0

x^2 + 3x - 2x - 6 =0

x(x+3) - 2(x-3) = 0

(x+3)(x-2) = 0

x = -3

x = 2

Hope it helped you

Answer 2

i think you know the basic algorithm which is
$log(m) + log(n) = log(mn)$
so,
x(x+1)=6
x^2+x-6=0
its your eqn now you can solve it easily