If `f` is a function satisfying `f(x+y)=f(x)xxf(y)` for all `x ,y in N` such that `f(1)=3` and `sum_(x=1)^nf(x)=120 ,` find the value of `n` .

Explanation

To solve the problem, we start with the functional equation given:

1. **Functional Equation**:
We have \( f(x+y) = f(x) \cdot f(y) \) for all \( x, y \in \mathbb{N} \) and \( f(1) = 3 \).

2. **Identifying the Function**:
We can assume a form for \( f(n) \). A common function that satisfies this type of equation is \( f(n) = a^n \).
Let's assume \( f(n) = a^n \).
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