1.
Let f(x)f(x) be a real differentiable function such that f(0)=1f(0) = 1 and f(x+y)=f(x)f′(y)+f′(x)f(y)f(x + y) = f(x)f'(y) + f'(x)f(y) for all x,y∈Rx, y \in \mathbb{R}. Then log⁡ef(5050)\log_e f(5050) is equal to: