Question

Calcule o valor do logaritmo:

Answer 1

Calcular logartimos

Lembrando que base e argumento iguais = 1

a)

$\sf \log_{3}~\dfrac{1}{9}$

$\sf \log_{3}~9^{-1}$

$\sf \log_{3}~(3^2)^{-1}$

$\sf \log_{3}~3^{-2}$

$\sf - 2\log_{3}~3$

$\sf - 2*1$

$\red{\sf = - 2}$

b)

$\sf \log_{2}~\dfrac{1}{32}$

$\sf \log_{2}~32^{-1}$

$\sf \log_{2}~(2^5)^{-1}$

$\sf \log_{2}~2^{-5}$

$\sf - 5\log_{2}~2$

$\sf - 5*1$

$\red{\sf = - 5}$

c)

$\sf \log_{3}~\dfrac{1}{27}$

$\sf \log_{3}~27^{-1}$

$\sf \log_{3}~(3^3)^{-1}$

$\sf \log_{3}~3^{-3}$

$\sf - 3\log_{3}~3$

$\sf - 3*1$

$\red{\sf = - 3}$

d)

$\sf \log_{5}~\dfrac{1}{125}$

$\sf \log_{5}~125^{-1}$

$\sf \log_{5}~(5^3)^{-1}$

$\sf \log_{5}~5^{-3}$

$\sf - 3\log_{5}~5$

$\sf - 3*1$

$\red{\sf = - 3}$