If is a function satisfying for all such that and

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

1. If

f

is a function satisfying

f(x+y)=f(x) f(y)

for all

x, y \in \mathbf{N}

such that

f(1)=3

and

\sum_{x=1}^{n} f(x)=120

, find the value of

n