Question

The value of ${\log }_{2}7$ is:

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

Answer 1

Answer: (D)

an irrational number

Suppose ${\log }_{2}7$ is rational.

$\Rightarrow {\log }_{2}7=\frac{a}{b}\Rightarrow 7=2^{a/b}$

$\Rightarrow 7^b=2^a$

But $2^a$ is even and $7^b$ is odd.

Hence, our assumption is wrong.

$\Rightarrow {\log }_{2}7$ is irrational.