The quadratic equation is giving me error can you please help me locate where I am wrong Question. Solve $$\log(x-3) + \log (x-4) - \log(x-5)=0.$$ 
Attempt. I got $$x^2-8x+17=0.$$
$$\log(x-3)(x-4)/(x-5)=0$$
$$\log(x^2-4x-3x+12)/x-5=0$$
$$x^2-7x+12= 10^0 (x-5)$$
$$x^2-7x-x+12+5=0$$
$$x^2-8x+17=0$$
Hi guys update: apparently the answer was equation is undefined‍♀️

What's the problem? We have\begin{align}\log(x-3)+\log(x-4)-\log(x-5)=0&\iff\log\bigl((x-3)(x-4)\bigr)=\log(x-5)\\&\iff\log(x^2-7x+12)=\log(x-5)\\&\iff x^2-7x+12=x-5\\&\iff x^2-8x+17=0.\end{align}
