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  4. If A is the number of integers, the logarithm of whose reciprocal to the base 4 have characterstic -3 , then the value of A is equal to

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Q. If $A$ is the number of integers, the logarithm of whose reciprocal to the base 4 have characterstic -3 , then the value of $A$ is equal to

Continuity and Differentiability

Solution:

$ -3 \leq \log _4\left(\frac{1}{N}\right)<-2$
$\Rightarrow -3 \leq-\log _4 N <-2 $
$\Rightarrow 2<\log _4 N \leq 3 $
$\Rightarrow 16< N \leq 64 $
$A =64-16=48 $