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  4. Let f ( n )= log 1155( n 3) for all n ∈ N, then find the value of f (7)+ f (11)+ f (15).

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Q. Let $f ( n )=\log _{1155}\left( n ^3\right)$ for all $n \in N$, then find the value of $f (7)+ f (11)+ f (15)$.

Continuity and Differentiability

Solution:

We have, $f ( n )=3 \log _{1155}( n ) $
$\therefore f (7)+ f (11)+ f (15)=3\left(\log _{1155}(7)+\log _{1155}(11)+\log _{1155}(15)\right) $
$=3 \log _{1155}(7 \times 11 \times 15)=3 \log _{1155}(1155)=3$