Question

Sabendo que log20 2 = a e log20 3 = b, calcule, em função de a e b:
(a) log6 18
(b) log12 25

Answer 1

Resposta:

Explicação passo a passo:

Usando mudança de base:

(a) log₆ 18 = log₂₀ 18/log₂₀ 6

log₂₀ (2.9)/log₂₀ (2.3) =

(log₂₀ 2 + log₂₀ 9)/(log₂₀ 2 + log₂₀ 3) =

(log₂₀ 2 + log₂₀ 3²)/(log₂₀ 2 + log₂₀ 3) =

(log₂₀ 2 + 2log₂₀ 3)/(log₂₀ 2 + log₂₀ 3) =

(a + 2b)/(a + b).

(b) log₁₂ 25 = log₂₀ 25/log₂₀ 12

log₂₀ 5²/log₂₀ (4.3) =

2(log₂₀ 5)/(log₂₀ 2² + log₂₀ 3) =

2(log₂₀ 20/4)/(2log₂₀ 2 + log₂₀ 3)=

2(log₂₀ 20 - log₂₀ 4)/(2log₂₀ 2 + log₂₀ 3) =

2(log₂₀ 20 - log₂₀ 2²)/(2log₂₀ 2 + log₂₀ 3) =

2(log₂₀ 20 - 2log₂₀ 2)/(2log₂₀ 2 + log₂₀ 3)=

2(1 - 2a)/(2a + b).