Question

Sendo f(x)=log3 x calcule:
a) f (27) =
b) f(1/81) =
c) (729)=

Answer 1

Para resolver esse exercícios você vai precisar saber algumas propriedades de log e equação exponencial.

$f(x)=log_{3} x$

a)

x = 27

$f_{(27)}=log_{3}27\\log_{3}27 = x$

$27=3^{x} \\3^{3}= 3^{x} \\x=3$

$f_{(27)}=3$

b)

$f_{(1/81)}=log_{3}^{1/81} \\\\log_{3}^{1/81}=log_{3} ^{1}-log_{3} ^{81}\\\\log_{3} ^{1}=x\\x=0\\\\log_{3} ^{81}=y\\81=3^{y} \\3^{4}= 3^{y} \\y=4\\\\log_{3}^{1/81}=-4$

$f_{(1/81)}=-4$

c)

$f_{(729)}=log_{3}^{729}\\log_{3}^{729}=x\\729=3^{x}\\3^{9}=3^{x} \\x=9$

$f_{(729)}=9$