SOLUTION: Prove by contradiction log2 11 is irrational. I'm a little stuck. Thank you.

Question 1206127: Prove by contradiction log2 11 is irrational. I'm a little stuck. Thank you.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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Prove by contradiction log2 11 is irrational. I'm a little stuck. Thank you.
~~~~~~~~~~~~~~~~~~~~

Let assume that    is a rational number

     = ,


where m and n are integer numbers.  Then

     = 11.


Raise both sides of this equation to degree n.  You will get

     = .    (*)


But 2 and 11 are relatively prime numbers.

So, equality (*) CONTRADICTS to the basic theorem of arithmetic
about uniqueness of the decomposition of integer numbers into a product of primes.

The proof is complete.

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