Modification of a logarithmic function with an infinite product equation

Question

I have the following logarithmic equation: $$y(x)=\ln\left(\prod_{n=1}^{\infty }(x-a_{n})\right)$$ To find the roots of $y(x)$, we put $$\prod_{n=1}^{\infty }(x-a_{n})=1$$ because, as you know, $\ln(f(x))=0$ if $f(x)=1$. Unfortunately, this will complicate things. Is there any mathematical trick to include a one inside the log equation so that we obtain $$\ln\left(\prod_{n=1}^{\infty }(x-a_{n})+1\right)=0$$ through which we achieve $$\prod_{n=1}^{\infty }(x-a_{n})+1=1$$ leading to eliminate the two ones and thus to obtain $$\prod_{n=1}^{\infty }(x-a_{n})=0$$.