We wszystkich przykładach dziedziną jest R a) [latex]2^{x+4} = 4^{x-3}[/latex] [latex]2^{x+4} = 2^{2(x-3)}[/latex] [latex]x+4 =2(x-3)[/latex] [latex]x+4 =2x-6[/latex] [latex]x-2x=-6-4[/latex] [latex]-x=-10 /:(-1)[/latex] [latex]x=10[/latex] -------------------------- b) [latex]5^{3x-1} = 125^{2-4x}[/latex] [latex]5^{3x-1} = 5^{3(2-4x)}[/latex] [latex]3x-1 = 3(2-4x)[/latex] [latex]3x-1 = 6-12x[/latex] [latex]3x+12x= 6+1[/latex] [latex]15x= 7 /:15[/latex] [latex]x= frac{7}{15}[/latex] -------------------------- c) [latex]81^{x^2+x}=3^{-2}[/latex] [latex]3^{4(x^2+x)}=3^{-2}[/latex] [latex]4(x^2+x)=-2 /:2[/latex] [latex]2(x^2+x)=-1[/latex] [latex]2x^2+2x+1=0[/latex] [latex]Delta=2^2-4 cdot 2 cdot 1=4-8=-4<0[/latex] Równanie nie ma rozwiązania -------------------------- d) [latex](0,125)^{5x-1}=64^{-7x+2}[/latex] [latex]left(frac{1}{8} ight) ^{5x-1}=8^{2(-7x+2)}[/latex] [latex]8^{-(5x-1)}=8^{2(-7x+2)}[/latex] [latex]-(5x-1)=2(-7x+2)[/latex] [latex]-5x+1=-14x+4[/latex] [latex]-5x+14x=4-1[/latex] [latex]9x=3 /:9[/latex] [latex]x= frac{1}{3}[/latex]
