Question

The number $\log_{2}7$is

• A. An integer
• B. A rational number
• C. An irrational number
• D. A prime number

Answer 1

Answer: (C)

An irrational number

Answer 2

Suppose, if possible, $\log_{2}7$is rational, say $p/q$where p and q are integers, prime to each other.

Then, $\frac{p}{q} = \log_{2}7 \Rightarrow 7 = 2^{p/q} \Rightarrow 2^{p} = 7^{q}$,

Which is false since L.H.S is even and R.H.S is odd. Obviously $\log_{2}7$ is not an integer and hence not a prime number