Question

sabendo que log2 = 0,3, o valor de
$log100 \sqrt[3]{400}$
é:
a) 13/30
b)4/30
c)11/45
d)3/4
e)1/2
​

Answer 1

Resposta:

43/15

Explicação passo-a-passo:

Resolvi supondo que o 100 é um fator do logaritmando, e a base sendo 10.

$log100 \sqrt[3]{400} \\ log( {10}^{2} . {400}^{ \frac{1}{3} } ) \\ log( {10}^{2}.(10.10.4)^{ \frac{1}{3} } ) \\ log( {10}^{2} . {10}^{ \frac{1}{3}} . {10}^{ \frac{1}{3} }. {4}^{ \frac{1}{3} } ) \\ log( {10}^{2 + \frac{2}{3} } . {4}^{ \frac{1}{3} } ) \\ log( {10}^{ \frac{8}{3} } . {4}^{ \frac{1}{3} } ) \\ log( {10}^{ \frac{8}{3} } ) + log( {4}^{ \frac{1}{3} } ) \\ \frac{8}{3} . log(10) + \frac{1}{3} . log(4) \\ \frac{8}{3} .1 + \frac{1}{3} . log( {2}^{2} ) \\ \frac{8}{3} + 2. \frac{1}{3} . log(2) \\ \frac{8}{3} + \frac{2}{3} .(0.3) \\ \frac{8}{3} + \frac{2}{3} . \frac{3}{10} \\ \frac{8}{3} + \frac{2}{10} \\ \frac{10 \times 8 + 3 \times 2}{30} \\ \frac{80 + 6}{30} \\ \frac{86}{30} \\ \frac{86 \div 2}{30 \div 2} \\ \frac{43}{15}$