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  4. If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N

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Q. If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N

Continuity and Differentiability

Solution:

We have $1 \cdot 2 \leq \log _{32} N \leq 1 \cdot 8 \Rightarrow 32^{1+\frac{1}{5}} \leq N \leq 32^{1+\frac{4}{5}} \Rightarrow 64 \leq N \leq 512$
Hence, number of integral values of $N = 512 - 63 = 449$