milangrg944 milangrg944

26-02-2020
Mathematics

contestada

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

=1

Respuesta :

alymary41 alymary41

26-02-2020

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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