Question

Ecuatie logaritmica:
$log _{x} 2+log _{ \sqrt{x} } 2=9$

Answer 1

x>0;  x diferit de 1.
Folosim proprietatea $\log_ab=\log_{a^2}{b^2}$ si obtinem:
$\log_x2+log_x{2^2}=9\Rightarrow\log_x2+2\log_x2=9\Rightarrow 3\log_x2=9\Riightarrow$
⇒$\log_x2=3\Rightarrow x^3=2\Rightarrow x=\sqrt[3]2$