Question

Resolva:

log X na base 3 + log 3X na base 3 + 1=0

Answer 1

Olá,

$\log_{3}x+\log_{3}3x+1=0\\ \log_{3}(x*3x)=-1\\\\ 3^{-1}=3x^2\\ \frac{1}{3} =3x^2\\ x^2= \frac{1}{9} \\ \\\boxed{\boxed{x= \pm \frac{1}{3} }}$

Condição de existência:

3x² > 0
x² > 0
x > 0

Answer 2

$log_3x+log_33x+1=0 \\ \\log_3(x*3x)=-1 \\ \\3^-^1 = 3x^2 \\ \\3^-^1 = \frac{1}{3^1}= \frac{1}{3} \\ \\ \frac{1}{3}=3x^2 \\ \\x^2 = \frac{1}{9} \\ \\x = \left \ {{+} \atop {-}} \right. \sqrt{ \frac{1}{9} } \\ \\x = \left \ {{+} \atop {-}} \right. \frac{1}{3} \\ \\S = [ -\frac{1}{3}, \frac{1}{3}} ]$

Espero ter ajudado. Valeu!