Question

3-Sabendo que Log 3(pequeno) 4 acima dele = 1,26, calcule (Dica: faça a mudança de base para base 3)

a)log4 3

b)log 12 3

Answer 1

Explicação passo-a-passo:

Lembre-se que:

$\text{log}_{a}~b=\dfrac{\text{log}_{c}~b}{\text{log}_{c}~a}$

a) $\text{log}_{4}~3=\dfrac{\text{log}_{3}~3}{\text{log}_{3}~4}$

$\text{log}_{4}~3=\dfrac{1}{1,26}$

$\text{log}_{4}~3=0,79$

b) $\text{log}_{12}~3=\dfrac{\text{log}_{3}~3}{\text{log}_{3}~12}$

Veja que:

$\text{log}_{3}~12=\text{log}_{3}~(4\cdot3)$

$\text{log}_{3}~12=\text{log}_3~4+\text{log}_3~3$

$\text{log}_{3}~12=1,26+1$

$\text{log}_{3}~12=2,26$

Então:

$\text{log}_{12}~3=\dfrac{1}{2,26}$

$\text{log}_{12}~3=0,44$