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13 November, 13:27

If a=b^x, b=c^y and c = a^z prove that xyz

=1

+1
Answers (1)
  1. 13 November, 16:52
    0
    If ax=b and by=c, substituting you get that axy=c. Now, if cz=a, substituting again, axyz=a, from where it follows that xyz=1.

    or

    c = {b^y} = [ (a^x) ^y] = {a^ (xy) }

    a = [c^z] = [{a^ (xy) }^z] = [a^ (xyz) ]

    (a^1) = [a^ (xyz) ]

    Therefore, (xyz) = 1.
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