If the graph of the function $y=f\left(x\right)$ has a unique tangent at the point $\left(a,0\right)$ through which the graph passes, then evaluate ${\left(\text{lim}\right)}_{x\vec{a}}\frac{{\left(\log \right)}_e\left\{1+6f\left(x\right)\right\}}{3f\left(x\right)}$

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