Question

considerando log 2 = 0,3 e log 3 = 0,48 , calcule os seguintes logaritmos
$\sqrt[3]{30?}$
log 144
​

Answer 1

Explicação passo a passo:

a) ³√30

log(³√30) = log(30)/3

30 = 3*10

log(30) = log(3) + log(10)

log(30) = 0.48 + 1 = 1.48

log(³√30) = 1.48/3 = 0.49333...

b) log(144)

144 2

72 2

36  2

18   2

 9   3

 3   3

 1

144 = 2^4 * 3^2

log(144) = 4log(2) + 2log(3)

log(144) = 4*0.3 + 2*0.48 = 2.16

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log\:2 = 0,3}$

$\mathsf{log\:3 = 0,48}$

$\mathsf{log\:\sqrt[3]{30} = log\:(3.10)^{\frac{1}{3}}}$

$\mathsf{log\:\sqrt[3]{30} = \dfrac{1}{3}\left(0,48 + 1\right)}$

$\mathsf{log\:\sqrt[3]{30} = \dfrac{1,48}{3}}$

$\boxed{\boxed{\mathsf{log\:\sqrt[3]{30} = 0,493}}}$

$\mathsf{log\:144 = log\:2^4.3^2}$

$\mathsf{log\:144 = 4\:log\:2 + 2\:log\:3}$

$\mathsf{log\:144 = 4(0,3) + 2(0,48)}$

$\mathsf{log\:144 = 1,2 + 0,96}$

$\boxed{\boxed{\mathsf{log\:144 = 2,16}}}$