Question

What is $\log 5$? How can we find logs of numbers without using a calculator?

Answer 1

Value of $\mathbf{log}\mathbf{}\mathbf{5}$ without using a calculator:

The value of $\log 5$ can be found using the logarithmic table.

$\log 5$ can be expressed as:

$$\begin{gathered} \log 5=\log \left(\frac{10}{2}\right) \\ \Rightarrow \log 5=\log 10-\log 2\left[\because log\left|\frac{m}{n}\right|=log\left|m\right|-log\left|n\right|,n\ne 0\right] \\ \Rightarrow \log 5=1-\log 2\left[\because log10=1\right] \\ \Rightarrow \log 5=1–0.3010\left[\because log2=0.3010\right] \\ \therefore \log 5=0.6990 \end{gathered}$$

Thus, the value of $\mathbf{log}\mathbf{}\mathbf{5}$ is $\mathbf{0}\mathbf{.}\mathbf{6990}$. The logs of numbers can be found using the logarithmic table.