anonymous
  • anonymous
How can i show that: a^x=e^(x*ln(a))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you don't really show it, that is the definition of \(a^x\)
anonymous
  • anonymous
but i suppose you could write \[\large e^{x\ln(a)}=e^{\ln(a^x)}=a^x\]
anonymous
  • anonymous
But i didnt understood it very well... why is that

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primeralph
  • primeralph
|dw:1377572731694:dw|
anonymous
  • anonymous
how would you define \[2^{\sqrt{2}}\] for example ?
primeralph
  • primeralph
|dw:1377572773055:dw|
primeralph
  • primeralph
|dw:1377572796811:dw|
anonymous
  • anonymous
\(\sqrt2\) is not a fraction so you cannot say "power and root" the definition of \[2^{\sqrt2}\] is \[e^{\sqrt2\ln(2)}\]
anonymous
  • anonymous
what you are using is the property of the log that says \[x\ln(a)=\ln(a^x)\] and also the fact that \[e^{\ln(whatever)}=whatever\]
anonymous
  • anonymous
that is what i dint understand: eln(whatever)=whatever
anonymous
  • anonymous
that explains, in that order, the two equal signs here \[\large e^{x\ln(a)}=e^{\ln(a^x)}=a^x\]
anonymous
  • anonymous
oh ok that is because \(f(x)=e^x\) and \(g(x)=\ln(x)\) are inverse functions so \[e^{\ln(x)}=\ln(e^x)=x\]
anonymous
  • anonymous
Oh sorry... I really got it... XD... thanks so much... Now it's clear. Thanks again

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