Question

The number $\log_{2} 7$ is

Easy

Solution

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.

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