[tex]\displaystyle\mathsf{log_{4}(x) *(log_{4}(x) +log_{4}( \frac{1}{16} ) )=3}\\\displaystyle\mathsf{[ODZ:x > 0]}\\\displaystyle\mathsf{log_{4}(x) *(log_{4}(x) +log_{2^2}( 2^{-4} ) )=3}\\\displaystyle\mathsf{log_{4}(x) *(log_{4}(x) -2 )=3}\\\displaystyle\mathsf{log_{4}(x)*log_{4}(x)-2log_{4}(x)=3}\\\displaystyle\mathsf{log^2_{4}(x)-2log_{4}(x)=3}\\\\\displaystyle\mathsf{[Zamena:t=log_{4}(x)]}\\[/tex]

[tex]\displaystyle\mathsf{t^2-2t=3}\\\displaystyle\mathsf{t^2-2t-3=0}\\\displaystyle\mathsf{D=b^2-4ac=(-2)^2-4*1*(-3)-12+4=16.}\\\displaystyle\mathsf{\sqrt{D} =\sqrt{16} =4.}\\\displaystyle\mathsf{t_{1} =\frac{2-4}{2}= -1.}\\\displaystyle\mathsf{t_{2} =\frac{2+4}{2}=3.}[/tex]

[tex]\displaystyle\mathsf{\left \{ {{log_{4}(x)=-1= > x_{1}=\frac{1}{4} . } \atop {log_{4}(x)=3= > x_{2} =64.}}} \right.[/tex]

Вітаю.

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