Question

log de 125 na base 0,04 é igual a x

Answer 1

$\log_{0,04}(125)=x\\\\ (0,04)^x=125\\\\ \left( \dfrac{4}{100}\right)^x=5^3~~(divide~por~4)\\\\ \left( \dfrac{1}{25}\right)^x=5^3\\\\ \left( \dfrac{1}{5^2}\right)^x=5^3\\\\ (5^{-2})^x =5^3\\ 5^{-2x}=5^3\\\\ \not 5^{-2x}=\not5^3\\\\ -2x=3\\\\ x=- \dfrac{3}{2}\\\\\\ \Large\boxed{\text{S}=\left\{- \dfrac{3}{2} \right\} }$