Question

Dados log2= 0,301, log3= 0,477 e log7= 0,845 calcule!
a) log15
b) log 42
c) log 0,6
d)14

Answer 1

(a)
$\log{15} = \log( \frac{3}{2} \cdot 10 ) = \log( \frac{3}{2} ) + \log{10} \\ \log{15} = \log{3} - \log{2} + \log{10} \\ \log{15}= 0,477 - 0,301 + 1 = 1,176$

(b)

$\log{42} = \log(7 \cdot 6) = \log(7 \cdot 3 \cdot 2) \\ \log{42} = \log{7} + \log{3} + \log{2} \\ \log{42} = 0,845 + 0,477 + 0,301 \\ \log{42} = 0,845 + 0,778 = 1,623$

(c)

$\log{0,6} = \log( \frac{6}{10} ) = \log{6} - \log{10} \\ \log{0,6} = \log(2 \cdot 3) - \log{10} \\ \log{0,6} = \log{2} + \log{3} - \log{10} \\ \log{0,6} = 0,301 + 0,477 - 1 \\ \log{0,6} = 0,778 - 1 = -0,222$

(d)

$\log{14} = \log(2 \cdot 7) = \log{2} + \log{7} \\ \log{14} = 0,301 + 0,845 = 1,146$