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Q.
Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N. If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is
$ f ( x + y )= f ( x ) \cdot f ( y ) \forall x , y \in N , f (1)=3$
$ f (2)= f ^2(1)=3^2$
$ f (3)= f (1) f (2)=3^3$
$f (4)=3^4$
$f ( k )=3^{ k } $
$\displaystyle \sum_{ k =1}^{ n } f ( k )=3279$
$ f (1)+ f (2)+ f (3)+\ldots \ldots \ldots+ f ( k )=3279$
$ 3+3^2+3^3+\ldots \ldots \ldots 3^{ k }=3279$
$ \frac{3\left(3^{ k }-1\right)}{3-1}=3279 $
$ \frac{3^{ k }-1}{2}=1093$
$ 3^{ k }-1=2186 $
$ 3^{ k }=2187 $
$k =7$