The approximate value of log (2.01), given that log 2 = 0.6934 is

$$\begin{gathered} \mathrm{x}=2 \delta x=0.01 \mathrm{f}\left(\mathrm{x}\right)=\log \mathrm{x} \\ \mathrm{f}(\mathrm{x}+\delta x)={\mathrm{f}}^1\left(\mathrm{x}\right).\delta x+\mathrm{f}\left(\mathrm{x}\right) \\ =\frac{1}{\mathrm{x}} \delta x+\mathrm{f}\left(\mathrm{x}\right) \\ =0.5\times 0.01+0.6934 \\ =0.005+0.6934 \\ =0.6984 \end{gathered}$$