Question

Log 0,25 raiz de 4 elevado a 5, calcule:

Answer 1

$log_{0.25} (\sqrt[5](4) = log_{{1 \over 4}} (4^{{1 \over 5}}) \\\\ log_{{1 \over 4}}(4^{{1 \over 5}}) = { 1 \over 5}log_{4^{-1}}(4) \\\\ { 1 \over 5}log_{4^{-1}}(4) = { 1 \over 5 } \times -1 log_4(4) \\\\ { 1 \over 5 } \times -1 log_4(4) = - {1 \over 5} \times 1 \\\\ \boxed {log_{0.25}(\sqrt[5](4) = (-5)^{-1} = -0,2}$