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Question

The number log2 7 is

A
An integer
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B
A rational number
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C
An irrational number
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D
A prime number
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Solution

The correct option is C An irrational number
Suppose, if possible, log2 7 is rational, say pq where p and q are integers, prime to each other.
Then, pq=log2 77=2pq2p=7q
which is false since L.H.S is even and R.H.S is odd.
Obviously log2 7 is not an integer and hence not a prime number.

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