Question

${\log }_{2}7$ is

• A. an integer
• B. a prime number
• C. a rational number
• D. an irrational number

Answer 1

The correct option is D an irrational number

Let ${\log }_{2}7$ be a rational number.
$\Rightarrow {\log }_{2}7=\left(\frac{p}{q}\right)$
$\Rightarrow 2^{\frac{p}{q}}=7\Rightarrow 2^p=7^q$
Here p and q being the integers cannot satisfy the above relation.
Hence ${\log }_{2}7$ is an irrational number.