if a=b^x,b=c^y and c= a^z prove that xyz =1 ​

Question

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

=1

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Remi 1 week 2021-11-16T07:59:46+00:00 1 Answer 0 views 0

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    2021-11-16T08:01:42+00:00

    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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