Question

Se 4^a = 12^b, quanto vale a/b? (Dica: Utilize a aproximação log4 3 ∼ 0, 8.)

Answer 1

Resposta:

$\dfrac{a}{b}=2,25$

Explicação passo-a-passo:

Com base nas propriedades do logaritmo, temos:

$log_{3}4 \approx0,8$

$4^a=12^b\\\\log_{12}4^a=b\\\\\dfrac{log_{3}4^a}{log_{3}12}=b\\\\\\\dfrac{log_{3}4^a}{log_{3}(4.3)}=b\\\\\\\dfrac{log_{3}4^a}{log_{3}4+log_{3}3}=b\\\\\\\dfrac{a\ . \ log_{3}4}{log_{3}4+log_{3}3}=b\\\\\\\dfrac{a\ . \ 0,8}{0,8+1}=b\\\\\\\dfrac{0,8a}{1,8}=b\\\\0,8a=1,8b\\\\\dfrac{a}{b}=\dfrac{1,8}{0,8}\\\\\dfrac{a}{b}=2,25$