Question

Calcule aplicando a definição

a) log 16 =
1/4

b) log √128 =
2

c) log 256 =
4

d) log 1 =
9

Answer 1

Resposta:

a) -2

b) 7/2

c) 4

d) 0

Explicação passo a passo:

a)

$log 16_{1/4} = x\\1/4^{x} = 16\\1/4^{x} = 1/4^{-2} \\x = -2$

b)

$log \sqrt{128} _{2} = x\\2^{x} = \sqrt{128} \\2^{x} = \sqrt{2^{7}}\\(2^{x} )^{2} = 2^{7}\\2^{2x} = 2^{7}\\2x = 7\\x = 7/2$

c)

$log 256_{4} = x\\(2^{2})^{x} = 256\\2^{2x} = 2^8\\2x = 8\\x = 4$

d)

$log 1_{9} = x\\9^{x} = 1\\9^{x} = 9^{0}\\x = 0$