Rozwiąż równanie: [latex]log_xsqrt{5}+ log_x(5x)-2,25=(log_xsqrt{5})^{2}[/latex]

[latex]log_xsqrt{5}+ log_x(5x)-2,25=(log_xsqrt{5})^{2}\ log_x5^{frac{1}{2}}+log_x5+log_xx-2,25=(log_x5^{frac{1}{2}})^2\ [/latex] [latex]frac{1}{2}*log_x5+log_x5+1-2,25=(frac{1}{2}*log_x5)^2\ frac{3}{2}*log_x5-frac{1}{4}*(log_x5)^2-1,25=0\ -frac{1}{4}*(log_x5)^2+frac{3}{2}*log_x5-1,25=0\ [/latex] [latex]-(log_x5)^2+6*log_x5-5=0\ t=log_x5\ -t^2+6*t-5=0\ Delta=36-20=16\ sqrtDelta=4\ t_1=1\ t_2=5\ 1) log_x5=1\ x^1=5\ x=5\ [/latex] [latex]2)log_x5=5\ x^5=5\ x=sqrt[5]{5}[/latex] Odp: x=5 lub x=[latex]sqrt[5]{5}[/latex]