Question

Resolva a equação log x na base 27 × log x na base 9 = 2/3

Answer 1

Resposta:

S = { 1/9, 9}

Explicação passo-a-passo:

$Log_{27}x.Log_9x = 2/3\\Log_{3^3}x.Log_{3^2}x = 2/3\\1/3.Log_3x.1/2.Log_3x = 2/3\\1/6.Log_3x.Log_3x = 2/3\\Log_3x.Log_3x = 2/3 / 1/6\\Log_3x^2 = 2/3.6\\Log_3x^2 = 12/3\\Log_3x^2 = 4\\Log_3x = +-\sqrt{4}\\Log_3x = +-2\\\\x' = 3^2\\x' = 9\\\\x'' = 3^{-2}\\x'' = 1/9$

Dúvidas só perguntar!