[tex] log_{2}(x) + log_{x}(2) = 2[/tex]
[tex] log_{2}(x) + \frac{1}{ log_{2}(x) } = 2[/tex]
[tex] log_{2}(x) = t, \: t > 0[/tex]
[tex]t + \frac{1}{t} = 2[/tex]
[tex]t + \frac{1}{t} - 2 = 0 \: | \times t[/tex]
[tex] {t}^{2} + 1 - 2t = 0[/tex]
[tex] {t}^{2} - 2t + 1 = 0[/tex]
[tex] {(t - 1)}^{2} = 0[/tex]
[tex] t - 1 = 0 = > t = 1[/tex]
[tex] log_{2}(x) = 1 = > x = 2[/tex]
