Question

Logaritmos -Considerando
log2 = 0,30
log3 = 0,48
log7 = 0,85
Determine:

a) Log(108/7)
b) Log2,4
c Log(49/144)

Answer 1

Explicação passo-a-passo:

Boa tarde, vamos aplicar as propriedades dos logaritmos:

a)

$log( \frac{108}{4} ) = log(108) - log(7)$

$= log(27 \times 4) - 0.85$

$= log(27) + log(4) - 0.85$

$= log( {3}^{3} ) + log( {2}^{2} ) - 0.85$

$= 3 log(3) + 2 log(2) - 0.85$

$= 3(0.48) + 2(0.3) - 0.85$

$= 1.44 + 0.6 - 0.85$

$= 1.19$

b)

$log(2.4) = log( \frac{24}{10} )$

$= log(24) - log(10)$

$= log(3 \times {2}^{3} ) - 1$

$= log(3) + 3 log(2) - 1$

$= 0.48 + 3(0.3) - 1$

$= 0.48 + 0.9 - 1$

$= 0.38$

c)

$log( \frac{49}{144} ) = log( \frac{7}{12} {)}^{2}$

$= 2( log(7) - log(12) )$

$2(0.85 - log( {2}^{2} \times 3 ) )$

$2(0.85 - (2 log(2) + log(3) ))$

$2(0.85 - (2(0.3) + 0.48))$

$2(0.85 - (1.08))$

$= 2(0.23)$

$= 0.46$