Proof by contradiction
How do I prove that log 12 to the base 8 is irrational?
And also with log 3 to the base 7?
Thanks!
And also with log 3 to the base 7?
Thanks!
You're trying to prove is irrational right?
Hint:
Hint 2:
Hint:
Spoiler
Hint 2:
Spoiler
(edited 6 years ago)
Original post by etothepiiplusone
You're trying to prove is irrational right?
Hint:
Hint 2:
Hint:
Spoiler
Hint 2:
Spoiler
I understand the general procedure but I am just stuck at this point. I said it can be expressed as p/q. After laws of logs and simplifying, I get to 8^n=12^m. I split it into factors but I am unsure what to do next
Original post by ElDonCorleone
I split it into factors
Show your working for this part
Original post by etothepiiplusone
Show your working for this part
Original post by ElDonCorleone
Ah just realised my powers should be swapped around... 8^n and 12^m...problem still stands
Original post by ElDonCorleone
Try getting it into the form
then think about this equation ( and will be integers).
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