Question

What is the value of $\log 7$ base $2$.

Answer 1

Find the logarithmic value.

$$\begin{gathered} {\log }_{2}7=\frac{\ln 7}{\ln 2}\left[\because {\log }_{a}b=\frac{\ln b}{\ln a}\right] \\ \Rightarrow {\log }_{2}7=\frac{1.946}{0.693}[\text{From log table}\ln 7=1.946\text{and}\ln 2=0.693] \\ \Rightarrow {\log }_{2}7~2.808 \end{gathered}$$

Hence, the value of ${\log }_{2}7$ is approximately $2.808$.