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

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To solve the problem, we need to find the value of \( n \) given that the function \( f \) satisfies the equation \( f(x+y) = f(x)f(y) \) for all \( x, y \) in \( X \), \( f(1) = 3 \), and the sum \( \sum_{x=1}^{n} f(x) = 120 \). ### Step 1: Understand the function's property The functional equation \( f(x+y) = f(x)f(y) \) suggests that \( f \) is an exponential function. A common form for such functions is \( f(x) = f(1)^x \). Given \( f(1) = 3 \), we can hypothesize that: \[ f(x) = 3^x \] ...
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