Question

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

• A. 0
• B. 1
• C. 7
• D. 9

Answer 1

Answer: (C)

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