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 need to find the value of \( n \) given the function \( f \) that satisfies the equation \( f(x+y) = f(x) \cdot f(y) \) for all \( x, y \in \mathbb{N} \) and the condition \( f(1) = 3 \). We also know that the sum \( \sum_{x=1}^{n} f(x) = 120 \).

### Step-by-Step Solution:

1. **Understanding the Functional Equation**:
The equation \( f(x+y) = f(x) \cdot f(y) \) suggests that \( f \) is an exponential function. This is a common form for functions that exhibit multiplicative behavior.

2. **Substituting Values**:
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