Question

How do you calculate $\log \left(0.1\right)$?

Answer 1

Calculate the given expression:

Given expression: $\log \left(0.1\right)$.

$0.1$ can be written in standard form as ${10}^{-1}$.

Thus, $\log \left(0.1\right)=\log \left({10}^{-1}\right)$.

As, $\log \left(b^a\right)=\log \left[b·b·b......·b(a\mathrm{times})\right]=\log \left(b\right)+\log \left(b\right)+\log \left(b\right)+...+\log \left(b\right)\left(a\mathrm{times}\right)$

Thus, $\mathbf{log}\left(b^{\mathit{a}}\right)\mathbf{=}\mathit{a}\mathbf{log}\left(b\right)$.

$\Rightarrow \log \left(0.1\right)=\left(-1\right)\log \left(10\right)$

It is known that $\log \left(10\right)=1$.

$$\begin{gathered} \Rightarrow \log \left(0.1\right)=\left(-1\right)\times 1 \\ \Rightarrow \log \left(0.1\right)=\left(-1\right) \end{gathered}$$

Therefore, $\log \left(0.1\right)=(-1)$.