Question

How do you evaluate $\log 0.01$?

Answer 1

Find the value of $\log 0.01$

Since, the base of the logarithm is not given we assume it to be $10$

$\Rightarrow$$\log 0.01={\log }_{10}0.01$

$\Rightarrow$$\log 0.01={\log }_{10}{10}^{-2}$ $...[\because 0.01={10}^{-2}]$

$\Rightarrow$$\log 0.01=-2\left({\log }_{10}10\right)$ $...[\because \log \left(a^m\right)=m\log a]$

$\Rightarrow$$\log 0.01=-2$ $...[\because {\log }_{a}a=1]$

Hence the value of $\log 0.01$ is $-2$