вправа 2.2 гдз 11 клас математика Мерзляк Номіровський 2019
Вправа 2.2
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\begin{equation} 1)0,4^{x^{2}-x-6}=1; \end{equation} \begin{equation} 0,4^{x^{2}-x-6}=0,4^{6}; \end{equation} \begin{equation} x^{2}-x-6=0; \end{equation} \begin{equation} x_{1}=3; x_{2}=-2; \end{equation} \begin{equation} 2)(\frac{3}{5})^{x}=\frac{5}{3}; \end{equation} \begin{equation} (\frac{3}{5})^{x}=(\frac{3}{5})^{-1}; \end{equation} \begin{equation} x=-1; \end{equation} \begin{equation} 3)0,7^{x}=2\frac{2}{49}; \end{equation} \begin{equation} 0,7^{x}=0,7^{x}=\frac{100}{49}; \end{equation} \begin{equation} 0,7^{x}=0,7^{-2}; \end{equation} \begin{equation} x=-2; \end{equation} \begin{equation} 4)9^{-x}=27; \end{equation} \begin{equation} (3^{2})^{-x}=3^{3}; \end{equation} \begin{equation} 3^{-2x}=3^{3}; \end{equation} \begin{equation} -2x=3; \end{equation} \begin{equation} x=-\frac{3}{2}; \end{equation} \begin{equation} 5)\sqrt{2^{x}}=8^{-\frac{2}{3}}; \end{equation} \begin{equation} (2^{x})^{\frac{1}{2}}=(2^{3})^{-\frac{2}{3}}; \end{equation} \begin{equation} 2^{\frac{1}{2}x}=2^{-2}; \end{equation} \begin{equation} \frac{1}{2}x=-2; \end{equation} \begin{equation} x=-4; \end{equation} \begin{equation} 6) (\frac{2}{9})^{2x+3}=4,5^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{45}{10})^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{9}{2})^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{9}{2})^{x-2}; \end{equation} \begin{equation} 2x+3=x-2; \end{equation} \begin{equation} x=-5; \end{equation} \begin{equation} 7)(\frac{2}{5})^{x}*(\frac{25}{8})^{x}=\frac{125}{64}; \end{equation} \begin{equation} (\frac{2}{5}*\frac{25}{8})^{x}=(\frac{5}{4})^{3}; \end{equation} \begin{equation} (\frac{5}{4})^{x}=(\frac{5}{4})^{3}; \end{equation} \begin{equation} x=3; \end{equation} \begin{equation} 8)32^{\frac{3}{5}x-2}=4^{6-\frac{3}{2}x}; \end{equation} \begin{equation} (2^{5})^{\frac{3}{5}x-2}=(2^{2})^{6-\frac{3}{2}x}; \end{equation} \begin{equation} 2^{3x-10}=2^{12-3x}; \end{equation} \begin{equation} 3x-10=12-3x; \end{equation} \begin{equation} 6x=22; x=\frac{22}{6}; \end{equation} \begin{equation} x=\frac{11}{3}; \end{equation} \begin{equation} 9)3^{x^{2}-9}=7^{x^{2}-9}; \end{equation} \begin{equation} \frac{3^{x^{2}-9}}{7^{x^{2}-9}}= \end{equation} \begin{equation} =\frac{7^{x^{2}-9}}{7^{x^{2}-9}}; \end{equation} \begin{equation} (\frac{3}{7})^{x-9}=1; \end{equation} \begin{equation} x^{2}-9=0; \end{equation} \begin{equation} x^{2}-9=0; \end{equation} \begin{equation} x^{2}=9; \end{equation} \begin{equation} x=\pm 3. \end{equation}
\begin{equation} 1)0,4^{x^{2}-x-6}=1; \end{equation} \begin{equation} 0,4^{x^{2}-x-6}=0,4^{6}; \end{equation} \begin{equation} x^{2}-x-6=0; \end{equation} \begin{equation} x_{1}=3; x_{2}=-2; \end{equation} \begin{equation} 2)(\frac{3}{5})^{x}=\frac{5}{3}; \end{equation} \begin{equation} (\frac{3}{5})^{x}=(\frac{3}{5})^{-1}; \end{equation} \begin{equation} x=-1; \end{equation} \begin{equation} 3)0,7^{x}=2\frac{2}{49}; \end{equation} \begin{equation} 0,7^{x}=0,7^{x}=\frac{100}{49}; \end{equation} \begin{equation} 0,7^{x}=0,7^{-2}; \end{equation} \begin{equation} x=-2; \end{equation} \begin{equation} 4)9^{-x}=27; \end{equation} \begin{equation} (3^{2})^{-x}=3^{3}; \end{equation} \begin{equation} 3^{-2x}=3^{3}; \end{equation} \begin{equation} -2x=3; \end{equation} \begin{equation} x=-\frac{3}{2}; \end{equation} \begin{equation} 5)\sqrt{2^{x}}=8^{-\frac{2}{3}}; \end{equation} \begin{equation} (2^{x})^{\frac{1}{2}}=(2^{3})^{-\frac{2}{3}}; \end{equation} \begin{equation} 2^{\frac{1}{2}x}=2^{-2}; \end{equation} \begin{equation} \frac{1}{2}x=-2; \end{equation} \begin{equation} x=-4; \end{equation} \begin{equation} 6) (\frac{2}{9})^{2x+3}=4,5^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{45}{10})^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{9}{2})^{x-2}; \end{equation} \begin{equation} (\frac{2}{9})^{2x+3}=(\frac{9}{2})^{x-2}; \end{equation} \begin{equation} 2x+3=x-2; \end{equation} \begin{equation} x=-5; \end{equation} \begin{equation} 7)(\frac{2}{5})^{x}*(\frac{25}{8})^{x}=\frac{125}{64}; \end{equation} \begin{equation} (\frac{2}{5}*\frac{25}{8})^{x}=(\frac{5}{4})^{3}; \end{equation} \begin{equation} (\frac{5}{4})^{x}=(\frac{5}{4})^{3}; \end{equation} \begin{equation} x=3; \end{equation} \begin{equation} 8)32^{\frac{3}{5}x-2}=4^{6-\frac{3}{2}x}; \end{equation} \begin{equation} (2^{5})^{\frac{3}{5}x-2}=(2^{2})^{6-\frac{3}{2}x}; \end{equation} \begin{equation} 2^{3x-10}=2^{12-3x}; \end{equation} \begin{equation} 3x-10=12-3x; \end{equation} \begin{equation} 6x=22; x=\frac{22}{6}; \end{equation} \begin{equation} x=\frac{11}{3}; \end{equation} \begin{equation} 9)3^{x^{2}-9}=7^{x^{2}-9}; \end{equation} \begin{equation} \frac{3^{x^{2}-9}}{7^{x^{2}-9}}= \end{equation} \begin{equation} =\frac{7^{x^{2}-9}}{7^{x^{2}-9}}; \end{equation} \begin{equation} (\frac{3}{7})^{x-9}=1; \end{equation} \begin{equation} x^{2}-9=0; \end{equation} \begin{equation} x^{2}-9=0; \end{equation} \begin{equation} x^{2}=9; \end{equation} \begin{equation} x=\pm 3. \end{equation}