Ответы
Ответ дал:
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третье задание:
1. ответ: x∈[–1,5; +∞)
![log_2(2x+7)\geq2\to\left[\begin{array}{ccc}2x+7\ \textgreater \ 0\\2x+7\geq4\end{array}\right\to\left[\begin{array}{ccc}x\ \textgreater \ -3,5\\x\geq-1,5\end{array}\right log_2(2x+7)\geq2\to\left[\begin{array}{ccc}2x+7\ \textgreater \ 0\\2x+7\geq4\end{array}\right\to\left[\begin{array}{ccc}x\ \textgreater \ -3,5\\x\geq-1,5\end{array}\right](https://tex.z-dn.net/?f=log_2%282x%2B7%29%5Cgeq2%5Cto%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2x%2B7%5C+%5Ctextgreater+%5C+0%5C%5C2x%2B7%5Cgeq4%5Cend%7Barray%7D%5Cright%5Cto%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C+%5Ctextgreater+%5C+-3%2C5%5C%5Cx%5Cgeq-1%2C5%5Cend%7Barray%7D%5Cright)
2. ответ: x∈(–∞; –3]
![log_{\frac{1}{5}}(2-x)\leq-1\to\left[\begin{array}{ccc}2-x\ \textgreater \ 0\\2-x\geq5\end{array}\right\to\left[\begin{array}{ccc}x\ \textless \ 2\\x\leq-3\end{array}\right log_{\frac{1}{5}}(2-x)\leq-1\to\left[\begin{array}{ccc}2-x\ \textgreater \ 0\\2-x\geq5\end{array}\right\to\left[\begin{array}{ccc}x\ \textless \ 2\\x\leq-3\end{array}\right](https://tex.z-dn.net/?f=log_%7B%5Cfrac%7B1%7D%7B5%7D%7D%282-x%29%5Cleq-1%5Cto%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2-x%5C+%5Ctextgreater+%5C+0%5C%5C2-x%5Cgeq5%5Cend%7Barray%7D%5Cright%5Cto%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C+%5Ctextless+%5C+2%5C%5Cx%5Cleq-3%5Cend%7Barray%7D%5Cright)
четвёртое задание:
1. ответ: x∈(
; +∞)
![2^{3x-2}\ \textgreater \ 8\ \textless \ =\ \textgreater \ 2^{3x-2}\ \textgreater \ 2^3\to3x-2\ \textgreater \ 3\to x\ \textgreater \ \frac{5}{3} 2^{3x-2}\ \textgreater \ 8\ \textless \ =\ \textgreater \ 2^{3x-2}\ \textgreater \ 2^3\to3x-2\ \textgreater \ 3\to x\ \textgreater \ \frac{5}{3}](https://tex.z-dn.net/?f=2%5E%7B3x-2%7D%5C+%5Ctextgreater+%5C+8%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+2%5E%7B3x-2%7D%5C+%5Ctextgreater+%5C+2%5E3%5Cto3x-2%5C+%5Ctextgreater+%5C+3%5Cto+x%5C+%5Ctextgreater+%5C+%5Cfrac%7B5%7D%7B3%7D)
2. ответ: x∈(–∞; 0,8]
![(\frac{1}{3})^{\frac{5}{4}x+3}\geq\frac{1}{81}\ \textless \ =\ \textgreater \ (\frac{1}{3})^{1,25x+3}\geq(\frac{1}{3})^4\to1,25x+3\leq4\to x\leq0,8 (\frac{1}{3})^{\frac{5}{4}x+3}\geq\frac{1}{81}\ \textless \ =\ \textgreater \ (\frac{1}{3})^{1,25x+3}\geq(\frac{1}{3})^4\to1,25x+3\leq4\to x\leq0,8](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B%5Cfrac%7B5%7D%7B4%7Dx%2B3%7D%5Cgeq%5Cfrac%7B1%7D%7B81%7D%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B1%2C25x%2B3%7D%5Cgeq%28%5Cfrac%7B1%7D%7B3%7D%29%5E4%5Cto1%2C25x%2B3%5Cleq4%5Cto+x%5Cleq0%2C8)
3. ответ: x∈(–∞;
)
![(\frac{1}{3^{2x+1}})^6\ \textgreater \ 9^{x-1}\ \textless \ =\ \textgreater \ 3^{-12x-6}\ \textgreater \ 3^{2x-2}\to-12x-6\ \textgreater \ 2x-2\to\\x\ \textless \ -\frac{2}{7} (\frac{1}{3^{2x+1}})^6\ \textgreater \ 9^{x-1}\ \textless \ =\ \textgreater \ 3^{-12x-6}\ \textgreater \ 3^{2x-2}\to-12x-6\ \textgreater \ 2x-2\to\\x\ \textless \ -\frac{2}{7}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%5E%7B2x%2B1%7D%7D%29%5E6%5C+%5Ctextgreater+%5C+9%5E%7Bx-1%7D%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+3%5E%7B-12x-6%7D%5C+%5Ctextgreater+%5C+3%5E%7B2x-2%7D%5Cto-12x-6%5C+%5Ctextgreater+%5C+2x-2%5Cto%5C%5Cx%5C+%5Ctextless+%5C+-%5Cfrac%7B2%7D%7B7%7D)
1. ответ: x∈[–1,5; +∞)
2. ответ: x∈(–∞; –3]
четвёртое задание:
1. ответ: x∈(
2. ответ: x∈(–∞; 0,8]
3. ответ: x∈(–∞;
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