Question

Calcule log4 81. Para isso, considere log 2 (aproximadamente igual) 0,301 e log 3 (aproximadamente igual) 0,477. Dica: utilize a propriedade mudança de base.​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Mudanc_{\!\!,}a\,de\,base}\\\sf \log_ba=\dfrac{\log_ca}{\log_bc}\\\\\sf \log_4{81}=\dfrac{\log81}{\log4}=\dfrac{\log3^4}{\log2^2}\\\\\sf\log_4{81}=\dfrac{\backslash\!\!\!4\log3}{\backslash\!\!\!2\log2}\\\\\sf \log_481=2\cdot\dfrac{\log3}{\log2}=2\cdot\dfrac{0,477}{0,301}\\\\\sf \log_4{81}=2\cdot1,58=3,16\end{array}}$