Question

If ${\log }_{10}2=0.3010$, the value of ${\log }_{10}80$ is

• A. $1.6020$
• B. $1.9030$
• C. $3.9030$
• D. None of these

Answer 1

The correct option is B

$1.9030$

Explanation for correct option:

Calculate the required logarithmic value

It is given that ${\log }_{10}2=0.3010$

So, the value of ${\log }_{10}80$ can be calculated as,

${\log }_{10}80={\log }_{10}\left(8\times 10\right)$

$\Rightarrow {\log }_{10}80={\log }_{10}8+{\log }_{10}10$ $\mathrm{[}\mathrm{\because }\mathrm{}\log \mathrm{(}\mathrm{m}\mathrm{\times }\mathrm{n}\mathrm{)}\mathrm{=}\mathrm{logm}\mathrm{+}\mathrm{logn}\mathrm{]}$

$\Rightarrow {\log }_{10}80={\log }_{10}{\left(2\right)}^3+{\log }_{10}10$

$\Rightarrow {\log }_{10}80=3\times {\log }_{10}2+{\log }_{10}10$ $\mathrm{[}\mathrm{\because }\mathrm{}\log {\left(m\right)}^{\mathrm{n}}\mathrm{=}\mathrm{nlogm}\mathrm{]}$

$\Rightarrow {\log }_{10}80=3\times 0.3010+{\log }_{10}10$

$\Rightarrow {\log }_{10}80=0.9030+{\log }_{10}10$

$\Rightarrow {\log }_{10}80=0.9030+1$ $\mathrm{[}\mathrm{}\mathrm{\because }{\log }_{\mathrm{10}}\mathrm{10}\mathrm{=}\mathrm{1}\mathrm{]}$

$\Rightarrow {\log }_{10}80=1.9030$

Hence, option (B) is the correct option.