Question

Dados log2 = 0,30 e log3 = 0,48, calcule usando as propriedades de logaritmos e os valores dados os seguintes itens.

a) log 0.0002 b) log 3√14,4 c) log50 d) log 72

Answer 1

a) log(0.0002)
$\log(2\times10^{-4})\\ \log(2)+\log(10^{-4})\\ \log(2)-4\log(10)\\ \log(2)-4\\ 0,30-4\\ -3,7$

b) log(3√14,4)
$\log(3(\frac{2^4\times 3^2}{10})^{ \frac{1}{2}})\\ \log(3)+\log((\frac{2^4\times 3^2}{10})^{ \frac{1}{2}})\\ \log(3)+ \frac{1}{2}(\log(2^4\times 3^2) - \log(10))\\ \log(3)+ \frac{1}{2}(4\log(2)+2\log(3)-\log(10))\\ 0,48+0,5(4\times0,30+2\times0,48-1)\\ 1,06$

c) log(50)
$\log(2\times 5^2)\\ \log(2)+\log(5^2)\\ \log(2)+2\times\log(5)\\ \log(2)+2\times\log(\frac{10}{2})\\ \log(2)+2(\log(10) - \log(2))\\ 0,30+2(1-0,30)\\ 1.7$

d) log(72)
$\log(2^3\times 3^2)\\ \log(2^3)+\log(3^2)\\ 3\log(2)+2\log(3)\\ 3\times0,30+2\times0,48\\ 1.86$