Question

Se log de x na base 3 + log de x na base 9 = 1, então o valor de x é:
a) ∛2.
b) √2.
c) ∛3.
d) √3.
e) ∛9.​

Answer 1

Resposta:

$\boxed{\mathtt{E}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\log_3 x + \log_9 x = 1} \\\\ \mathsf{\log_3 x + \log_{3^2} x = 1} \\\\ \mathsf{\log_3 x + \frac{1}{2} \cdot \log_3 x = 1} \\\\ \mathsf{\left ( 1 + \frac{1}{2} \right ) \cdot \log_3 x = 1} \\\\ \mathsf{\frac{3}{2} \cdot \log_3 x = 1} \\\\ \mathsf{3 \cdot \log_3 x = 2} \\\\ \mathsf{\log_3 x^3 = 2}$

$\\ \displaystyle \mathsf{3^2 = x^3} \\\\ \mathsf{x^3 = 9} \\\\ \boxed{\boxed{\mathsf{x = \sqrt[3]{9}}}}$