Question

Como fazer a conta: log 0,2 na base √25 ?

Answer 1

$\log_{\sqrt{25}}0{,}2\Longrightarrow\log_{5}0{,}2\\\\\\\log_50{,}2=x\Longleftrightarrow0{,}2=5^x\\\\\\\dfrac{2}{10}=5^x\\\\\\\dfrac{1}{5}=5^x\\\\\\5^{-1}=5^x\\\\\\\therefore\ x=-1\\\\\\\\\boxed{\log_{\sqrt25}0{,}2=-1}$