Предмет: Математика,
автор: Sasha9290
Логарифмы. Решите неравенства. №26, 27
Приложения:
Аноним:
26)1
27)12
Ответы
Автор ответа:
1
26)
![log_{0.5} (3x) \geq log_{0.5} (x+16) \\\\ x\ \textgreater \ 0; x\ \textgreater \ -16 \\ x\in(0;+\infty) \\\\ 3x \leq x+16 \\ 2x \leq 16 \\ x \leq 8 \\\\ x\in(0;8] \\\\ x=1](https://tex.z-dn.net/?f=log_%7B0.5%7D+%283x%29++%5Cgeq+log_%7B0.5%7D+%28x%2B16%29+%5C%5C%5C%5C+x%5C+%5Ctextgreater+%5C+0%3B+x%5C+%5Ctextgreater+%5C+-16+%5C%5C+x%5Cin%280%3B%2B%5Cinfty%29+%5C%5C%5C%5C+3x+%5Cleq+x%2B16+%5C%5C+2x+%5Cleq+16+%5C%5C+x+%5Cleq+8+%5C%5C%5C%5C+x%5Cin%280%3B8%5D+%5C%5C%5C%5C+x%3D1 "log_{0.5} (3x) \geq log_{0.5} (x+16) \\\\ x\ \textgreater \ 0; x\ \textgreater \ -16 \\ x\in(0;+\infty) \\\\ 3x \leq x+16 \\ 2x \leq 16 \\ x \leq 8 \\\\ x\in(0;8] \\\\ x=1")
27)
![log_{0.2} (4x-6) \geq log_{0.2}(x+33) \\\\ 4x-6\ \textgreater \ 0; x\ \textgreater \ 1.5 \\ x+33\ \textgreater \ 0; x\ \textgreater \ -33 \\ x\in(1.5;+\infty) \\\\ 4x-6 \leq x+33 \\ 3x \leq 39 \\ x \leq 13 \\\\ x\in(1.5;13] \\x=13](https://tex.z-dn.net/?f=log_%7B0.2%7D+%284x-6%29+%5Cgeq+log_%7B0.2%7D%28x%2B33%29+%5C%5C%5C%5C+4x-6%5C+%5Ctextgreater+%5C+0%3B+x%5C+%5Ctextgreater+%5C+1.5+%5C%5C+x%2B33%5C+%5Ctextgreater+%5C+0%3B+x%5C+%5Ctextgreater+%5C+-33+%5C%5C+x%5Cin%281.5%3B%2B%5Cinfty%29+%5C%5C%5C%5C+4x-6+%5Cleq+x%2B33+%5C%5C+3x+%5Cleq+39+%5C%5C+x+%5Cleq+13+%5C%5C%5C%5C+x%5Cin%281.5%3B13%5D+%5C%5Cx%3D13 "log_{0.2} (4x-6) \geq log_{0.2}(x+33) \\\\ 4x-6\ \textgreater \ 0; x\ \textgreater \ 1.5 \\ x+33\ \textgreater \ 0; x\ \textgreater \ -33 \\ x\in(1.5;+\infty) \\\\ 4x-6 \leq x+33 \\ 3x \leq 39 \\ x \leq 13 \\\\ x\in(1.5;13] \\x=13")
27)
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