Question

log3 x = 1 + log9 x​

Answer 1

Boa tarde!

$log_{3}x = 1 + log_{9}x \\ log_{3}x = 1 + \frac{ log_{3}x }{ log_{3}9 } \\ log_{3}x = 1 + \frac{ log_{3}x }{2} \\ log_{3}x = \frac{2}{2} + \frac{ log_{3}x }{2} \\ log_{3}x = \frac{ 2 + log_{3}x }{2} \\ 2.log_{3}x = 2 + log_{3}x \\ {log_{3}x}^{2} = 2 + log_{3}x \\ {log_{3}x}^{2} - log_{3}x = 2 \\ log_{3}( \frac{ {x}^{2} }{x} ) = 2 \\ log_{3}x = 2 \\ x = {3}^{2} \\ x = 9$

Espero ter ajudado!

Bons estudos!

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_3\:x = 1 + log_9\:x}$

$\mathsf{log_3\:x = 1 + log_{3^2}\:x}$

$\mathsf{log_3\:x = log_3\:3 + \dfrac{1}{2}\:.\:log_{3}\:x}$

$\mathsf{2\:log_3\:x = 2\:log_3\:3 + log_{3}\:x}$

$\mathsf{log_3\:x^2 = log_3\:9 + log_{3}\:x}$

$\mathsf{x^2 = 9x}$

$\mathsf{x^2 - 9x = 0}$

$\mathsf{x(x - 9) = 0}$

$\mathsf{x - 9 = 0}$

$\mathsf{x = 9}$

$\boxed{\boxed{\mathsf{S = \{9\}}}}$