Question

Qual é o valor de:
log72 - log12 - log27
(ambos todos na base 3)

Answer 1

log₃72 - log₃12 - log₃27

log₃8.3² - log₃4.3 - log₃3³

(log₃2³ + log₃3²) - (log₃2² + log₃3) - log₃3³

3log₃2 + 2log₃3 - 2log₃2 - log₃3 - 3log₃3

3log₃2 + 2.1 - 2log₃2 - 1 - 3.1

log₃2 - 2

Answer 2

Resposta:

1

Explicação passo-a-passo:

$log_{3}72 - log_{3}12 - log_{3}2\\log_{3}2^{3} . 3^{2} - log_{3} 2^{2} . 3 - log_{3} 2\\log_{3} 2^{3} + log_{3} 3^{2} - log_{3} 2^{2} + log_{3} 3 - log_{3}2\\3log_{3}2 - 2log_{3}3 - log_{3}2 + 2log_{3}3 - log_{3}3\\\\arrumando...\\3log_{3}2 - 2log_{3}2 - log_{3}2 + 2log_{3}3 + log_{3}3\\3log_{3}2 -3log_{3}2 + 2log_{3}3 + log_{3}3\\0 + log_{3}3\\\\Resultado:1$