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jane19

  • 4 years ago

how would you expand the given logarithm: log base 4 (³√z /16y^3)

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  1. y2o2
    • 4 years ago
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    is it \[\log_{4}({\sqrt[3]{z} \over 16y^3})\] ?

  2. jane19
    • 4 years ago
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    yes

  3. y2o2
    • 4 years ago
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    \[\log_{4}({\sqrt[3]{z} \over 16y^3}) = \log_{4}(\sqrt[3]{z})+\log_{4}({1 \over 16y^3}) =\\ {1 \over 3}\log_{4}({z})+\log_{4}(16^{-1}) + \log_{4}(y^{-3}) = \\ {1 \over 3}\log_{4}({z})-\log_{4}(4^2) - 3 \ \log_{4}(y) = \\ {1 \over 3}\log_{4}({z})-2- 3 \ \log_{4}(y)\]

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