CAT 2017 Slot 1 — QA Question 23

0.008 = 8/1000 = 1/125 = 5^-3

∴ log_0.008√5 = ${\log }_{5^{-3}}\left(5^{1/2}\right)$ = $\frac{1/2}{-3}$ = $\frac{-1}{6}$ and

log_√381 = ${\log }_{3^{1/2}}\left(3^4\right)$ = $\frac{4}{1/2}$ = 8.

∴ The given expression is -1/6 + 8 - 7 = 5/6

Hence, option (c).