I have a couple of properties that need to be proven.

Use the definition a^x = e^(x log a) to derive the following properties of general exponentials:

a) (ab)^x = (a^x)(b^x)

b) (a^x)(a^y) = a^(x+y)

c) (a^x)^y = (a^y)^x = a^(xy)

Thank you

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- May 7th 2007, 08:20 PMDudenOxfordLogs proofs
I have a couple of properties that need to be proven.

Use the definition a^x = e^(x log a) to derive the following properties of general exponentials:

a) (ab)^x = (a^x)(b^x)

b) (a^x)(a^y) = a^(x+y)

c) (a^x)^y = (a^y)^x = a^(xy)

Thank you - May 7th 2007, 08:26 PMalinailiescu
(ab)^x=e^(xlogab)=e^(x*(loga+logb))=e^(xloga+xlogb )=e^(xloga)*e^(xlogb)=a^x*b^x

Hope this gives you a hint how to do the other ones.

Alina