Question

Escreva em base 10: log2 80, considerando log2 ~- 0,3 e log5 ~- 0,7

Answer 1

$log_{2}(80) = \frac{ log(80) }{ log(2) } \\ \\ = \frac{ log( {2}^{4} \times 5 ) }{ log(2) } \\ \\ = \frac{ log( {2}^{4}) + log(5) }{ log(2) } \\ \\ \frac{4 log(2) + log(5) }{ log(2) }$

Se log2 = 0.3 e log5 =0.7 Então:


$\frac{(4 \times 0.3) + 0.7}{0.3} \\ \\ = \frac{1.2 + 0.7}{0.3} \\ \\ = \frac{1.9}{0.3} = \frac{ \frac{19}{10} }{ \frac{3}{10} } = \frac{19}{3} = 6.333...$