Folosim formula:
[tex] log_{a}b = \frac{1}{ log_{b} a} [/tex]
[tex] log_{4}(x) + \frac{1}{ log_{4} (x)}=2[/tex]
Notam: [tex] t = log_{4}(x) [/tex]
t + 1 / t = 2
Aducem la acelasi numitor
t² + 1 = 2t
t² - 2t + 1 = 0
[tex] t_{12}= \frac{2 +/- \sqrt{4 - 4} }{2} = \frac{2}{2} = 1[/tex]
[tex] log_{4}(x) = 1 => x = 4^{1} = 4 [/tex]
[tex]x=4[/tex]
