Question

Como resolvo esse logaritmo? Passo a passo.
log ∛2/2 na base 4


Answer 1

Vamos usar as seguintes propriedades:

$\displaystyle \log_{a} \frac{x}{y} = \\ \\ \\ \log_{a} x - \log_{a} y = \\ \\ \\ \frac{\ln x}{\ln a} - \frac{\ln y }{\ln a}$

Daí:

$\displaystyle \log_{4} \frac{ \sqrt[3]{2} }{2} \\ \\ \\ \hookrightarrow \log_{4} \sqrt[3]{2} - \log_{4} 2 \\ \\ \\ \hookrightarrow \frac{\ln \sqrt[3]{2} }{\ln 4} - \frac{\ln 2}{\ln 4} \\ \\ \\ \hookrightarrow \frac{0.23}{1.39} - \frac{0.69}{1.39} \\ \\ \\ \hookrightarrow \frac{0.23-0.69}{1.39} \\ \\ \\ \hookrightarrow \frac{-0.46}{1.39} \approx -0.33$