Răspunsuri

2014-08-13T18:33:49+03:00
Folosim formula:
 log_{a}b =  \frac{1}{ log_{b} a}

 log_{4}(x) +  \frac{1}{ log_{4} (x)}=2

Notam:  t = log_{4}(x)

t + 1 / t = 2
Aducem la acelasi numitor
t² + 1 = 2t
t² - 2t + 1 = 0

 t_{12}=  \frac{2 +/-  \sqrt{4 - 4} }{2}  =  \frac{2}{2} = 1

 log_{4}(x) = 1  =>  x =  4^{1}  = 4

x=4