1. Tardigrade
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  4. Let A denotes the Antilog 32(0.8) and B denotes the number of the integers which have the characteristic 4 when the base of log is 5 and C denotes the value of - log 7( log 3 √√[7]9) then unit digit of (A+B+C) is

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Q. Let A denotes the Antilog ${ }_{32}(0.8)$ and B denotes the number of the integers which have the characteristic 4 when the base of $\log$ is 5 and $C$ denotes the value of $-\log _7\left(\log _3 \sqrt{\sqrt[7]{9}}\right)$ then unit digit of $(A+B+C)$ is

Continuity and Differentiability

Solution:

$ A =\operatorname{Antilog}_{32}(0.8)=(32)^{0.8}=\left(2^5\right)^{\frac{4}{5}}=2^4=16$
$B =5^{4+1}-5^4=3125-625=2500 $
$C =-\log _7\left(\log _3 \sqrt{\sqrt[7]{9}}\right)=-\log _7\left(\log _3 9^{\frac{1}{14}}\right)=1 .$
So unit digit of $A + B + C$ is 7