Show that the number `log_2(7)` is an irrational number

Explanation

Let us assume given expression is a rational number.

Let `log_2(7) = p/q`

Here, `p/q` is a rational number.

`log_2(7) =p/q=>2^(p/q) = 7`

Raising both sides with power of `q`,

`2^(p/q**q) = 7^q=>2^p = 7^q`

As, `2^p` is always even and `7^q` is always odd.

So, our assumption is wrong that given expression is equal to a rational number.

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