Rozwiąż równania wykładnicze: a) [latex]( frac{2}{3} ) ^{x ^{2} -} ^{3x} = ( frac{9}{4} ) ^{x-3} [/latex] b) [latex]( frac{9}{ sqrt{3} } ) ^{x} = 3 ^{x+1} [/latex]

[latex]( frac{2}{3} ) ^{x ^{2} -} ^{3x} = ( frac{9}{4} ) ^{x-3} \ ( frac{2}{3} ) ^{x ^{2} -} ^{3x} = ( frac{3}{2} ) ^{2x-6} \ ( frac{2}{3} ) ^{x ^{2} -} ^{3x} = ( frac{2}{3} ) ^{-2x+6} \ x^2-3x=-2x+6\ x^2-3x+2x-6=0\ x(x-3)+2(x-3)=0\ (x+2)(x-3)=0\ x=-2 vee x=3[/latex] [latex]( frac{9}{ sqrt{3} } ) ^{x} = 3 ^{x+1} \ ( frac{3^2}{ 3^{frac{1}{2}} } ) ^{x} = 3 ^{x+1} \ ( 3^{1frac{1}{2}}) ^{x} = 3 ^{x+1} \ ( 3^{frac{3}{2}}) ^{x} = 3 ^{x+1} \ 3 ^{frac{3x}{2}} = 3 ^{x+1} \ frac{3x}{2}=x+1\ 3x=2x+2\ x=2[/latex]