\log_7n is either an integer or an irrational number

Vilharjevw7

Vilharjevw7

Answered question

2022-01-20

log7n is either an integer or an irrational number

Answer & Explanation

Rylee Marshall

Rylee Marshall

Beginner2022-01-21Added 6 answers

Interesting; usually one would assume not just that b doesn't divide a but that a and b are co', but in this case your assumption that b doesn't divide a is enough.
If 7ab=n, then 7a=nb. Thus n must be a power of 7, so we can write n=7k and thus 7a=7kb, so a=kb, contradicting the assumption.

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