If for all x, y N , there exists a function f(x) satisfying f(x+y)=f(x) f(y) such that f(1)=3 and _ x=1 ^n f(x)=120 , then value of n will be

Step-by-step solution

Given, for x, y Nf(x+y)=f(x) f(y) Then, function will be of the form f(x)=a^x , where a N [ a 1] array ll & f(1)=3 & f(1)=a^1=3 & a=3 array Function is f(x)=3^x . Now, _ x=1 ^n f(x)=120 _ x=1 ^n 3^x=120 3+3^2+3^3+ +3^n=120 3 (3^ n -1 ) 3-1 =120 array ll & 3^n=1+ 120 2 3 & 3^n=81=3^4 array So, n=4