Question

determine o valor da base a nas igualdades a seguir:

a)loga 8=3
b)loga 81=4
c)loga 1=0
d)loga 1/16=2

Answer 1

a)

$\log_a 8 = 3\\ \\a^3=8\\ \\a=\sqrt[3]{2^3}\\ \\a=2$

b)

$\log_a 81 = 4\\ \\a^4=81\\ \\a=\sqrt[4]{3^4}\\ \\a=3$

c)

$\log_a 1 = 0\\ \\a^0=1$

$S=\{a\in\mathbb{R}\ |\ 0<a\neq1 \}$

d)

$\log_a \frac{1}{16} = 2\\ \\a^2=\frac{1}{16}\\ \\a=\sqrt{\frac{1}{16}}\\ \\a=\frac{1}{4}$