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Prove that if a^x = b^y = (ab)^xy, then x + y = 1

Reply 1

ukdragon37

snoopyx

Prove that if a^x = b^y = (ab)^xy, then x + y = 1

Rewrite as

x\ln a = y \ln b = xy \ln \left(ab\right)

then consider

x\ln a = xy \ln \left(ab\right)

and

y \ln b = xy \ln \left(ab\right)

independently which should give you two equations that you can solve simultaneously for x and y with a and b eliminated.

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