Question

Rezolvati ec logaritmica:

$log_{x} 2 + log_{ \sqrt{x} } 2 = 9$

Answer 1

$log_x 2 + log_{\sqrt{x}} 2 = 9$
$log_x 2 + log_{x^ \frac{1}{2}} 2 = 9$
$log_x 2 + log_x 4 = 9$
$\frac{log_2 2}{log_2 x} + \frac{log_2 4}{log_2 x} = 9$
$\frac{1+2}{log_2 x} = 9$
3 = 9$log_2 x$
$log_2 x = \frac{1}{3}$
x = $\sqrt[3]{2}$