Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 520

\[\boxed{\mathbf{520}.}\]

\[1)\ 6^{2x} = 6^{\frac{1}{5}};\]

\[2x = \frac{1}{5}\]

\[x = \frac{1}{5} \bullet \frac{1}{2} = \frac{1}{10} = 0,1;\]

\[Ответ:\ \ x = 0,1.\]

\[2)\ 3^{x} = 27;\]

\[3^{x} = 3^{3}\]

\[\ x = 3;\]

\[Ответ:\ \ x = 3.\]

\[3)\ 7^{3x} = 7^{10};\]

\[3x = 10\]

\[\ x = \frac{10}{3} = 3\frac{1}{3};\]

\[Ответ:\ \ x = 3\frac{1}{3}.\]

\[4)\ 2^{2x + 1} = 32;\]

\[2^{2x + 1} = 2^{5};\]

\[2x + 1 = 5;\]

\[2x = 4\]

\[\ x = \frac{4}{2} = 2;\]

\[Ответ:\ \ x = 2.\]

\[5)\ 4^{2 + x} = 1;\]

\[4^{2 + x} = 4^{0};\]

\[2 + x = 0\]

\[x = - 2;\]

\[Ответ:\ \ x = - 2.\ \]