Question

Dado log2 = 0,3010 e log 3 = 4771 calcule log 5, log 1800, log 0,0072

Answer 1

$log(5) = log( \frac{10}{2} ) \\ \\ = log(10) - log(2)$
como sabemos que log(10) = 1 e que log(2) = 0,3010 Então:

$1 - 0.3010 = 0.699$



$log(1800) = log(18 \times 100 \\ \\ = log(2 \times {3}^{2} \times {10}^{2} ) \\ \\ = log(2) + log( {3}^{2} ) + log( {10}^{2} ) \\ \\ = log(2) + 2 log(3) + 2 log(10) \\ \\ = 0.3010 + 2(0.477) + 2(1) \\ \\ = 3.2551$



$log(0.0072) = log( \frac{72}{10000} ) \\ \\ = log( \frac{ {2}^{3} \times {3}^{2} }{ {10}^{4} } ) \\ \\ = log( {2}^{3} \times {3}^{2} ) - log( {10}^{4} ) \\ \\ = log( {2}^{3} ) + log( {3}^{2} ) - log( {10}^{4} ) \\ \\ = 3 log(2) + 2 log(3) - 4 log(10) \\ \\ = 3(0.3010) - 2(0.4771) + 4(1) \\ \\ = 5.8572$