Question

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

Answer 1

is it
\[\log_{4}({\sqrt[3]{z} \over 16y^3})\]
?

Answer 2

yes

Answer 3

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