I needed to replace a solution in the equation, to see if it was correct.
The two solutions of this equation: $log_5{(x+3)} + log_5{(12x + 1)} = 3$,
are: {${\frac{-61}{12}, 2}$}
The solution $2$, satisfy the equation, but with $\frac{-61}{12}$ is the problem.
My development to replace in a image:
In step 2, I specifically marked it with a circle. My teacher says that it does not satisfy, since there are no negative logarithms, but if I continue to develop the equation, it remains as positive and if it satisfies, then who is wrong?
The conditions of the equation are
$$x+3>0$$ and $$12x+1>0.$$
which could be replaced by $$x>\frac {-1}{12} $$
but $$\frac {-61}{12}<\frac {-1}{12} $$ and is not a solution.