Question

sa se rezolve ecuatia logaritmica:

$2 lg^{2} ( x^{3} ) - 3lg x - 1 = 0$

Answer 1

$2lg^2x^3-3lgx-1=0$
$2(lgx^3)^2-3lgx-1=0$
$2(3lgx)^2-3lgx-1=0$
$2*9lg^2x-3lgx-1=0$; Notam lg x cu a 
$18a^2-3a-1 = 0$

$a_1 = \frac{1}{3}$
$a_2 = \frac{-1}{6}$

$lg x = \frac{1}{3}$ => x = $\sqrt[3]{10}$
$lg x = \frac{-1}{6}$ => x = $\frac{1}{ \sqrt[6]{10} }$