Question

What is $\log \left(200\right)$?

Answer 1

Value of $\mathbf{log}\mathbf{}\mathbf{\left(}\mathbf{200}\mathbf{\right)}$:

$\log \left(200\right)$ can be written as follow:

$$\begin{gathered} \log 200=\log (2\times 100) \\ =\log 2+\log 100\mathbf{}\left[\because log\left|m\right|+log\left|n\right|=log\left|mn\right|\right] \\ =\log 2+\log {10}^2 \\ =\log 2+2\log 10\mathbf{}\mathbf{}\left[\because log{\left|m\right|}^n=nlog\left|m\right|\right] \\ =0.30103+2\times 1 \\ =2.30103 \end{gathered}$$

Thus, the value of $\mathbf{log}\mathbf{}\mathbf{\left(}\mathbf{200}\mathbf{\right)}$ is $\mathbf{2}\mathbf{.}\mathbf{3013}$