Question

Considerando o log 2 = x, calcule, em função de x: a) log 4096 b) log (raiz cúbica)512 c) log (raiz de sete)128 d) log 25,6 O prazo é hoje, agradeço com 100 pontos!

Answer 1

Explicação passo-a-passo:

Lembre-se que:

$\sf log_{b}~a^n=n\cdot log_{b}~a$

$\sf \sqrt[c]{a^b}=a^{\frac{b}{c}}$

$\sf log_{b}~\dfrac{a}{c}=log_{b}~a-log_{b}~c$

a) $\sf log~4096=log~2^{12}$

$\sf log~4096=12\cdot log~2$

$\sf log~4096=12x$

b) $\sf log~\sqrt[3]{512}=log~2^{\frac{9}{3}}$

$\sf log~\sqrt[3]{512}=log~2^3$

$\sf log~\sqrt[3]{512}=3\cdot log~2$

$\sf log~\sqrt[3]{512}=3x$

c) $\sf log~\sqrt[7]{128}=log~2^{\frac{7}{7}}$

$\sf log~\sqrt[7]{128}=log~2$

$\sf log~\sqrt[7]{128}=x$

d) $\sf log~25,6=log~\dfrac{256}{10}$

$\sf log~25,6=log~256-log~10$

$\sf log~25,6=log~2^8-1$

$\sf log~25,6=8\cdot log~2-1$

$\sf log~25,6=8x-1$