Решить логарифмическое уравнение:
[tex]lg ^{2} x - \frac{51}{8 \sqrt{ lg^{2} x - lgx} } = lgx - 2[/tex]
[tex]lg ^{2} x - \frac{51}{8 \sqrt{ lg^{2} x - lgx} } = lgx - 2[/tex]
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Z=√(lg^2(x)-lg(x))z^2+2=51/8z
8z^3+16z-51=0
(2z-3)(4z^2+6z+17)=0
z=3/2 вторая скобка без корней.
√(lg^2(x)-lg(x))=3/2
lg^2(x)-lg(x)-9/4=0
lg(x)=1/2+-√10/2
x=10^(1/2+-√10/2)