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anonymous

  • one year ago

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]

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  1. anonymous
    • one year ago
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    And I guess also, what is the principle here that allows it to be true?

  2. anonymous
    • one year ago
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    Oh and does the base make any difference? If b/n = Log_E[a] then b = Log_E[a^n]

  3. JoannaBlackwelder
    • one year ago
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    Yep, that is true. It is the exponent rule.

  4. JoannaBlackwelder
    • one year ago
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    |dw:1432883340617:dw|

  5. JoannaBlackwelder
    • one year ago
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    It is true for the same reason that when you raise an exponent to another exponent, they multiply.

  6. anonymous
    • one year ago
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    Got it, T/Y, So I could just quote 'the exponent rule' as an explanation for where this applies

  7. JoannaBlackwelder
    • one year ago
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    I think the technical name is the logarithmic power rule.

  8. JoannaBlackwelder
    • one year ago
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    yw :-)

  9. anonymous
    • one year ago
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    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)

  10. JoannaBlackwelder
    • one year ago
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    Yep :-)

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