Logarithmic Equation: How to solve for x

Question

Equation: $$\log_a (x) + \log_a (x-4) = \log_a (x+6)$$

Progress

$$\log_a (x^2-4x) = \log_a (x+6)$$ $$x^2-5x-6=0$$

Delta

$$x1= 6$$

$$x2=-1$$

Answer 1

Your first step is correct. Now, if you search only real solutions, you have $$ x^2-4x=x+6 $$ can you solve? (be care to the the acceptability of the solutions).

Answer 2

HINT: $$\log_a X = \log_a Y$$ implies $$X=Y$$

So in your case, you need to solve an equation.