The number log2 7 is
a irrational number.
Let us assume that log2 7 is rational, say pq where p and q are integers, prime to each other.
Then, pq=log2 7⇒7=2pq⇒2p=7q
which is false since L.H.S is even and R.H.S is odd.
Thus, log2 7 is not an integer and hence, not a prime number.