Question

Adotando log6 11=1,34 e log6 2 =0,37 calcule :
(A) log2 11
(B) log11 2
(C) log6 16

Answer 1

$\textsf{Para o log de um n\'umero elevado a uma pot\^encia vale a seguinte pr\underline{o}}\\\textsf{priedade:}\\\\\large\fbox{ \mathsf{\ell og_a~\alpha^{\beta}=\beta\ell og_a~\alpha} }\\\\\\\\\mathsf{Propriedade~para~mudan\c{c}a~de~base:}~~\large\fbox{ \mathsf{\ell og_a b=\dfrac{\ell og_cb}{\ell og_ca}} }$


$\mathsf{Adotando~log_611=1,34,~log_62=0,37~~e~aplicando~as~propriedades}\\\mathsf{acima~dispostas,~poderemos~calcular~os~seguintes~logaritmos:}\\\\\\\mathsf{log_211~\Leftrightarrow~\dfrac{log_6~11}{log_6~2}~\Leftrightarrow~\dfrac{1,34}{0,37}\approx 3,62}\\\\\\\mathsf{log_{11}2~\Leftrightarrow~\dfrac{log_6~2}{log_6~11}~\Leftrightarrow~\dfrac{0,37}{1,34}\approx 0,27}$


$\mathsf{log_6~16~\Leftrightarrow~log_6~2^4~\Leftrightarrow~4log_6~2~\Leftrightarrow~4\cdot 0,37\approx1,48}$