Question

Considerando que log base= 2 logaritmando= 5, aproximadamente 2, 32, obtenha o valor de:

β=(log base= 2 ∛0,2) × [ log base= 2(frac 64 sobre 125) ]

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_2\:5 = 2,32}$

$\mathsf{\beta = log_2\:\sqrt[3]{0,2} \times log_2\:\dfrac{64}{125}}$

$\mathsf{\beta = log_2\:\left(\dfrac{2}{10}\right)^{\frac{1}{3}} \times log_2\:\dfrac{2^6}{5^3}}$

$\mathsf{\beta = \dfrac{1}{3}.[log_2\:2 - (log_2\:2 + log_2\:5)] \times (6\:log_2\:2 - 3\:log_2\:5)}$

$\mathsf{\beta = \dfrac{1}{3}.[1 - (1 + 2,32)] \times [6(1) - 3(2,32)]}$

$\mathsf{\beta = \dfrac{1}{3}.[1 - 3,32] \times [6 - 6,96]}$

$\mathsf{\beta = -0,77 \times -0,96}$

$\boxed{\boxed{\mathsf{\beta = 0,74}}}$