Question

The Logarithm of $0.001$ to the base $10$ is equal to:

• A. $-1$
• B. $-3$
• C. $2$
• D. $6$

Answer 1

The correct option is B

$-3$

The explanation for the correct option.

We have to find the value of ${\log }_{10}0.001$.

As we know, ${\log }_{a}b=\frac{\log b}{\log a}$

$$\begin{gathered} \therefore {\log }_{10}0.001=\frac{\log 0.001}{\log 10} \\ \Rightarrow =\frac{\log {10}^{-3}}{\log 10}\left[\because 0.001={10}^{-3}\right] \\ \Rightarrow =\frac{-3\log 10}{\log 10}\left[\because \log a^b=b\log a\right] \\ \Rightarrow =-3 \end{gathered}$$

Hence, the option $B$is correct.