Question

The number $lo{g}_{2}7$ is

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

Answer 1

Answer: (C)

a irrational number.

Let us assume that $lo{g}_{2}7$ is rational, say $\frac{p}{q}$ where p and q are integers, prime to each other.

$Then,\frac{p}{q}=lo{g}_{2}7\Rightarrow 7=2^{\frac{p}{q}}\Rightarrow 2^p=7^q$
which is false since L.H.S is even and R.H.S is odd.
Thus, $lo{g}_{2}7$ is not an integer and hence, not a prime number.