Question

Considerando log 2≅ 0,3,log 3≅ 0,48 e log 5≅ 0,7 calcule o valor de:
​

Answer 1

Explicação passo-a-passo:

$a) log_{3}(2) = \frac{ log(2) }{ log(3) } = \frac{0.3}{0.48} = \frac{30}{48} = \frac{15}{24} = \frac{5}{8} = 0.625 \\ b) log_{5}(3) = \frac{ log(3) }{ log(5) } = \frac{0.48}{0.7} = \frac{48}{70} = \frac{24}{35} = 0.686 \\ c) log_{2}(5) = \frac{ log(5) }{ log(2) } = \frac{0.7}{0.3} = \frac{7}{3} = 2.333... \\ d) log_{3}(100) = \frac{ log(100) }{ log(3) } = \frac{ log( {10}^{3} ) }{0.48} = \frac{3 log(10) }{0.48} = \frac{3}{0.48} = \frac{300}{48} = \frac{150}{24} = \frac{75}{12} = 6.25$