Question

The number ${\log }_2\left(7\right)$ is

• A. Integer
• B. Rational number
• C. Irrational number
• D. Prime number

Answer 1

The correct option is C

Irrational number

Explanation for the correct option

Let $x={\log }_2\left(7\right)$

Then $2^x=7\left[\because {\log }_a\left(x\right)=y\mathrm{then}{\mathrm{b}}^{\mathrm{y}}=\mathrm{x}\right]$

This is only possible for irrational number

Hence, the correct option is $\left(\mathrm{C}\right)$.