Question

2) Determine o valor das bases (a) nas seguintes
igualdades:

Answer 1

Explicação passo-a-passo:

a)

$\sf log_{a}~64=3$

$\sf a^3=64$

$\sf a=\sqrt[3]{64}$

$\sf \red{a=4}$

b)

$\sf log_{a}~81=4$

$\sf a^4=81$

$\sf a=\sqrt[4]{81}$

$\sf \red{a=3}$

c)

$\sf log_{a}~\dfrac{1}{27}=-3$

$\sf a^{-3}=\dfrac{1}{27}$

$\sf \dfrac{1}{a^3}=\dfrac{1}{27}$

$\sf a^3=27$

$\sf a=\sqrt[3]{27}$

$\sf \red{a=3}$

d)

$\sf log_{a}~625=4$

$\sf a^4=625$

$\sf a=\sqrt[4]{625}$

$\sf \red{a=5}$

e)

$\sf log_{a}~\dfrac{1}{16}=-2$

$\sf a^{-2}=\dfrac{1}{16}$

$\sf \dfrac{1}{a^2}=\dfrac{1}{16}$

$\sf a^2=16$

$\sf a=\sqrt[2]{16}$

$\sf \red{a=4}$