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  4. Let p be the integral part of log 3 108 and q be the integral part of log 5 375 then (p+q-p q) has the value equal to

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Q. Let $p$ be the integral part of $\log _3 108$ and $q$ be the integral part of $\log _5 375$ then $(p+q-p q)$ has the value equal to

Continuity and Differentiability

Solution:

$4<\log _3 108<5 \Rightarrow p =4 $ and $ 3<\log _5 375<4 \Rightarrow q =3$
$\therefore p + q - pq =7-12=-5$.