Does L'H apply here?

Calculus Level 4

The graph of function \(y = f(x)\) has a unique tangent at \((e^a,0)\) through which the graph passes, then \(\displaystyle \lim_{x \to e^a} \cfrac{\log(1+7f(x)) - \sin (f(x))}{3f(x)}\) equals to

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