[tex] {4}^{x} + {2}^{x} = 6[/tex]
[tex] { ({2}^{2} )}^{x} + {2}^{x} - 6 = 0[/tex]
[tex] { ({2}^{x}) }^{2} + {2}^{x} - 6 = 0[/tex]
[tex] {2}^{x} = t \: \: \: ,t > 0[/tex]
[tex] {t}^{2} + t - 6 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = 1[/tex]
[tex]c = - 6[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {1}^{2} - 4 \times 1 \times ( - 6)[/tex]
[tex]\Delta = 1 + 24[/tex]
[tex]\Delta = 25[/tex]
[tex]t_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - 1 \pm \sqrt{25} }{2 \times 1} = \frac{ - 1 \pm5}{2} [/tex]
[tex]t_{1} = \frac{ - 1 + 5}{2} = \frac{4}{2} = 2 = > {2}^{x} = 2 = > x = 1[/tex]
[tex]t_{2} = \frac{ - 1 - 5}{2} = - \frac{6}{2} = - 3 \: nu \: convine[/tex]