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

1.	Show that the number `log_2(7)` is an irrational number
Answer» 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. Thus, `log_2(7)` is an irrational number.

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