document.write( "Question 1206127: Prove by contradiction log2 11 is irrational. I'm a little stuck. Thank you. \n" ); document.write( "

Algebra.Com's Answer #843366 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Prove by contradiction log2 11 is irrational. I'm a little stuck. Thank you.
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document.write( "Let assume that    is a rational number\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "where m and n are integer numbers.  Then\r\n" );
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document.write( "     = 11.\r\n" );
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document.write( "Raise both sides of this equation to degree n.  You will get\r\n" );
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document.write( "     = .    (*)\r\n" );
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document.write( "But 2 and 11 are relatively prime numbers.\r\n" );
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document.write( "So, equality (*) CONTRADICTS to the basic theorem of arithmetic\r\n" );
document.write( "about uniqueness of the decomposition of integer numbers into a product of primes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The proof is complete.\r
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