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Prove that number (log)2 7 is an irratio...

Prove that number `(log)_2 7` is an irrational number.

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Let ` log_(2) 7 ` is a rational number. Then,
` log_(2)7=p/q , p,q in Q or 7 = 2^(p//q) or 7^(q) = 2^(p)`
which is not possible for any integral values of p and q.
Hence, ` log_(2) 7 ` is not rational.
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-ILLUSTRATION 1.10
  1. Prove that number (log)2 7 is an irrational number.

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