Question

show that log7 is an irrational number using contradiction method​

Answer 1

Assume log7 is rational.

Let log7n = a/b

If $7^{\frac{a}{b}}= n 7^{\frac{a}{b}}= n,~ then~ 7^a=n^b.$

Thus n must be a power of 7.

So, we can write $n = 7^k$ and thus, $7^a = 7^{kb}$.

So, a = kb is contradicting the assumption.

Hence, log 7 is irrational.

Answer 2

Answer:

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