Question

(UFRGS – 2018)Se log3 x + log9 x = 1, então o valor de x é?

Answer 1

log3 x + log9 x = 1

log3 x + log3 x / log3 9 = 1

log3 x + log3 x / 2 = 1 ==> *(2)

2.log3 x + log3 x = 2

3log3 x = 2

log3 x³ = 2

x³ = 9

x = ³√9

Answer 2

Resposta:

$\boxed{\mathtt{\sqrt[3]{9}}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\log_3 x + \log_9 x = 1} \\\\ \mathsf{\log_3 x + \log_{3^2} x = 1} \\\\ \mathsf{\log_3 x + \frac{1}{2} \cdot \log_3 x = 1} \\\\ \mathsf{\log_3 x \cdot \left ( 1 + \frac{1}{2} \right ) = 1} \\\\ \mathsf{\frac{3}{2} \cdot \log_3 x = 1} \\\\ \mathsf{3 \cdot \log_3 x = 2} \\\\ \mathsf{\log_3 x^3 = 2} \\\\ \mathsf{3^2 = x^3} \\\\ \mathsf{x^3 = 9} \\\\ \boxed{\boxed{\mathsf{x = \sqrt[3]{9}}}}$