Question

3^2x = (6*3^x  -3)/2 e doar la puterea x , nu x-3 

Answer 1

Notam pe $3^{x}=a$
Si atunci avem $3^{2x}=(3^{x})^{2}$
Ecuatia devine
$a^{2}=\frac{6a-3}{2}\Rightarrow 2a^{2}=6a-3\Rightarrow 2a^{2}-6a+3=0$
Gasim solutiile ecuatiei ca pentru oricare functie de gradul II
$\Delta=36-4*2*3=36-24=12$
$a1=\frac{6-\sqrt{12}}{2*2}=\frac{6-2\sqrt{3}}{4}$
$a2=\frac{6+\sqrt{12}}{2*2}=\frac{6+2\sqrt{3}}{4}$
Atunci solutiile ecuatiei sunt:
$3^{x1}=\frac{6-2\sqrt{3}}{4}\Rightarrow x1=\log_{3}{\frac{6-2\sqrt{3}}{4}}$
$3^{x2}=\frac{6+2\sqrt{3}}{4}\Rightarrow x2=\log_{3}{\frac{6+2\sqrt{3}}{4}}$