Răspuns:
[tex]a \times 3 ^ { x } + 3 ^ { - x } = 5[/tex]
[tex]a\times 3^{x}=5-3^{-x} [/tex]
[tex]3^{x}a=-\frac{1}{3^{x}}+5 [/tex]
[tex]\frac{3^{x}a}{3^{x}}=\frac{5\times 3^{x}-1}{3^{x}\times 3^{x}} [/tex]
[tex]a=\frac{5\times 3^{x}-1}{3^{x}\times 3^{x}} [/tex]
[tex]a=\frac{5\times 3^{x}-1}{3^{2x}} [/tex]
Rezolvare x:
[tex]\left\{\begin{matrix}x=\frac{\ln(\frac{\sqrt{25-4a}+5}{a})-\ln(2)}{\ln(3)}\text{, }&a>0\text{ and }a\leq \frac{25}{4}\\x=\log_{3}\left(-\frac{\sqrt{25-4a}-5}{2a}\right)\text{, }&a\neq 0\text{ and }a\leq \frac{25}{4}\\x=-\log_{3}\left(5\right)\text{, }&a=0\end{matrix}\right.[/tex]
