anonymous
  • anonymous
What is the name of the rule that allows this to be true? And is it actually true? If b/n = Log[a] then b = Log[a^n]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
And I guess also, what is the principle here that allows it to be true?
anonymous
  • anonymous
Oh and does the base make any difference? If b/n = Log_E[a] then b = Log_E[a^n]
JoannaBlackwelder
  • JoannaBlackwelder
Yep, that is true. It is the exponent rule.

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JoannaBlackwelder
  • JoannaBlackwelder
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JoannaBlackwelder
  • JoannaBlackwelder
It is true for the same reason that when you raise an exponent to another exponent, they multiply.
anonymous
  • anonymous
Got it, T/Y, So I could just quote 'the exponent rule' as an explanation for where this applies
JoannaBlackwelder
  • JoannaBlackwelder
I think the technical name is the logarithmic power rule.
JoannaBlackwelder
  • JoannaBlackwelder
yw :-)
anonymous
  • anonymous
Ah I see, so Log power rule... if n=3 Log (a^n) = Log(a^3) = Log(a . a . a) = Log(a) + Log(a) + Log(a) = 3 Log(a) and because 1 = 3 Log(a) 1/3 = 3 Log(a) /3 1/3 = Log(a)
JoannaBlackwelder
  • JoannaBlackwelder
Yep :-)

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