Question

Find the value of $\log {}_5$ $0.008$

Answer 1

${\log }_{5}0.008=x$

or, $0.008=5^x$

or, $5^x=\frac{8}{1000}$

or, $5^x=\frac{1}{125}=\frac{1}{5^3}$

or, $5^x=5^{-3}$

$\therefore x=-3$

$\therefore {\log }_{5}0.008=-3$