Question

Se ㏒₄3 = α, então ㏒₂₇108 é igual a:
(a) 4
(b) 3a
(c) (3a+1)/3a
(d) (a+3)/a
(e) 6

Answer 1

Resposta:

(c) (3a + 1)/(3a)

Explicação passo a passo:

108 = 2² · 3³

27 = 3³

log₂₇ 108 = (1/3) · log₃ (2² · 3³)

log₂₇ 108 = (1/3) · (log₃ 4 + log₃ 3³)

log₂₇ 108 = (1/3) · (1/log₄ 3 + 3)

log₂₇ 108 = (1/3) · (1/a + 3)

log₂₇ 108 = 1/3a + 1

log₂₇ 108 = (3a + 1)/(3a)

Answer 2

Resposta:

log27(108) = log27(4*27) = 1 + log27(4)

log4(3) = a

log4(27) = 3a

log27(4) = 1/(3a)

log27(108) = 1 + 1/(3a) = (3a + 1)/(3a) (C)