Question

log2 = 0,3010 e log3 = 0,4771, calcule: log 8 600 mude a base para 10

Answer 1

Temos o seguinte:

$\mathtt{log_{8}(600) = \dfrac{log_{10}(600)}{log_{10} (8)} }$

Assim temos:

$\mathtt{log_{10}(600) = log_{10}(10^2*2*3) = 2log_{10}(10) + log_{10}(2) + log_{10}(3)} \\ \\ \mathtt{2log_{10}(10) + log_{10}(2) + log_{10}(3) =2*1 + 0,3010 + 0,4771 = 2,778}$

$\mathtt{log_{10}(8) = log_{10}(2^3) = 3log_{10}(2) = 3*0,3010 =0,903 }$

Logo:

$\mathtt{log_{8}(600) = \dfrac{log_{10}(600)}{log_{10} (8)} = \dfrac{2,778}{0,903} \approx 3,076 }$