2^x<=0 (неравенство)

Укажите решение неравенства: 2^x<=0 (множество решений неравенства)

Вы ввели

 x     
2  <= 0

$$2^{x} \leq 0$$

Подробное решение

Дано неравенство:
$$2^{x} \leq 0$$
Чтобы решить это нер-во - надо сначала решить соотвествующее ур-ние:
$$2^{x} = 0$$
Решаем:
$$x_{1} = -74.176760093132$$
$$x_{2} = -48.176760093132$$
$$x_{3} = -64.176760093132$$
$$x_{4} = -40.176760093132$$
$$x_{5} = -88.176760093132$$
$$x_{6} = -72.176760093132$$
$$x_{7} = -60.176760093132$$
$$x_{8} = -110.176760093132$$
$$x_{9} = -56.176760093132$$
$$x_{10} = -66.176760093132$$
$$x_{11} = -44.176760093132$$
$$x_{12} = -80.176760093132$$
$$x_{13} = -82.176760093132$$
$$x_{14} = -52.176760093132$$
$$x_{15} = -124.176760093132$$
$$x_{16} = -102.176760093132$$
$$x_{17} = -108.176760093132$$
$$x_{18} = -112.176760093132$$
$$x_{19} = -118.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -106.176760093132$$
$$x_{22} = -122.176760093132$$
$$x_{23} = -92.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -84.176760093132$$
$$x_{26} = -68.176760093132$$
$$x_{27} = -94.176760093132$$
$$x_{28} = -78.176760093132$$
$$x_{29} = -104.176760093132$$
$$x_{30} = -100.176760093132$$
$$x_{31} = -58.176760093132$$
$$x_{32} = -130.176760093132$$
$$x_{33} = -62.176760093132$$
$$x_{34} = -90.176760093132$$
$$x_{35} = -54.176760093132$$
$$x_{36} = -86.176760093132$$
$$x_{37} = -116.176760093132$$
$$x_{38} = -114.176760093132$$
$$x_{39} = -96.176760093132$$
$$x_{40} = -46.176760093132$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -50.176760093132$$
$$x_{43} = -98.176760093132$$
$$x_{44} = -76.176760093132$$
$$x_{45} = -70.176760093132$$
$$x_{46} = -42.176760093132$$
$$x_{1} = -74.176760093132$$
$$x_{2} = -48.176760093132$$
$$x_{3} = -64.176760093132$$
$$x_{4} = -40.176760093132$$
$$x_{5} = -88.176760093132$$
$$x_{6} = -72.176760093132$$
$$x_{7} = -60.176760093132$$
$$x_{8} = -110.176760093132$$
$$x_{9} = -56.176760093132$$
$$x_{10} = -66.176760093132$$
$$x_{11} = -44.176760093132$$
$$x_{12} = -80.176760093132$$
$$x_{13} = -82.176760093132$$
$$x_{14} = -52.176760093132$$
$$x_{15} = -124.176760093132$$
$$x_{16} = -102.176760093132$$
$$x_{17} = -108.176760093132$$
$$x_{18} = -112.176760093132$$
$$x_{19} = -118.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -106.176760093132$$
$$x_{22} = -122.176760093132$$
$$x_{23} = -92.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -84.176760093132$$
$$x_{26} = -68.176760093132$$
$$x_{27} = -94.176760093132$$
$$x_{28} = -78.176760093132$$
$$x_{29} = -104.176760093132$$
$$x_{30} = -100.176760093132$$
$$x_{31} = -58.176760093132$$
$$x_{32} = -130.176760093132$$
$$x_{33} = -62.176760093132$$
$$x_{34} = -90.176760093132$$
$$x_{35} = -54.176760093132$$
$$x_{36} = -86.176760093132$$
$$x_{37} = -116.176760093132$$
$$x_{38} = -114.176760093132$$
$$x_{39} = -96.176760093132$$
$$x_{40} = -46.176760093132$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -50.176760093132$$
$$x_{43} = -98.176760093132$$
$$x_{44} = -76.176760093132$$
$$x_{45} = -70.176760093132$$
$$x_{46} = -42.176760093132$$
Данные корни
$$x_{32} = -130.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{41} = -126.176760093132$$
$$x_{15} = -124.176760093132$$
$$x_{22} = -122.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{19} = -118.176760093132$$
$$x_{37} = -116.176760093132$$
$$x_{38} = -114.176760093132$$
$$x_{18} = -112.176760093132$$
$$x_{8} = -110.176760093132$$
$$x_{17} = -108.176760093132$$
$$x_{21} = -106.176760093132$$
$$x_{29} = -104.176760093132$$
$$x_{16} = -102.176760093132$$
$$x_{30} = -100.176760093132$$
$$x_{43} = -98.176760093132$$
$$x_{39} = -96.176760093132$$
$$x_{27} = -94.176760093132$$
$$x_{23} = -92.176760093132$$
$$x_{34} = -90.176760093132$$
$$x_{5} = -88.176760093132$$
$$x_{36} = -86.176760093132$$
$$x_{25} = -84.176760093132$$
$$x_{13} = -82.176760093132$$
$$x_{12} = -80.176760093132$$
$$x_{28} = -78.176760093132$$
$$x_{44} = -76.176760093132$$
$$x_{1} = -74.176760093132$$
$$x_{6} = -72.176760093132$$
$$x_{45} = -70.176760093132$$
$$x_{26} = -68.176760093132$$
$$x_{10} = -66.176760093132$$
$$x_{3} = -64.176760093132$$
$$x_{33} = -62.176760093132$$
$$x_{7} = -60.176760093132$$
$$x_{31} = -58.176760093132$$
$$x_{9} = -56.176760093132$$
$$x_{35} = -54.176760093132$$
$$x_{14} = -52.176760093132$$
$$x_{42} = -50.176760093132$$
$$x_{2} = -48.176760093132$$
$$x_{40} = -46.176760093132$$
$$x_{11} = -44.176760093132$$
$$x_{46} = -42.176760093132$$
$$x_{4} = -40.176760093132$$
являются точками смены знака неравенства в решениях.
Сначала определимся со знаком до крайней левой точки:
$$x_{0} \leq x_{32}$$
Возьмём например точку
$$x_{0} = x_{32} - \frac{1}{10}$$
=
$$-130.176760093132 - \frac{1}{10}$$
=
$$-130.276760093132$$
подставляем в выражение
$$2^{x} \leq 0$$
$$2^{-130.276760093132} \leq 0$$

6.06439490285985e-40 <= 0

но

6.06439490285985e-40 >= 0

Тогда
$$x \leq -130.176760093132$$
не выполняется
значит одно из решений нашего неравенства будет при:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$

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       x_32      x_24      x_41      x_15      x_22      x_20      x_19      x_37      x_38      x_18      x_8      x_17      x_21      x_29      x_16      x_30      x_43      x_39      x_27      x_23      x_34      x_5      x_36      x_25      x_13      x_12      x_28      x_44      x_1      x_6      x_45      x_26      x_10      x_3      x_33      x_7      x_31      x_9      x_35      x_14      x_42      x_2      x_40      x_11      x_46      x_4

Другие решения неравенства будем получать переходом на следующий полюс
и т.д.
Ответ:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$
$$x \geq -126.176760093132 \wedge x \leq -124.176760093132$$
$$x \geq -122.176760093132 \wedge x \leq -120.176760093132$$
$$x \geq -118.176760093132 \wedge x \leq -116.176760093132$$
$$x \geq -114.176760093132 \wedge x \leq -112.176760093132$$
$$x \geq -110.176760093132 \wedge x \leq -108.176760093132$$
$$x \geq -106.176760093132 \wedge x \leq -104.176760093132$$
$$x \geq -102.176760093132 \wedge x \leq -100.176760093132$$
$$x \geq -98.176760093132 \wedge x \leq -96.176760093132$$
$$x \geq -94.176760093132 \wedge x \leq -92.176760093132$$
$$x \geq -90.176760093132 \wedge x \leq -88.176760093132$$
$$x \geq -86.176760093132 \wedge x \leq -84.176760093132$$
$$x \geq -82.176760093132 \wedge x \leq -80.176760093132$$
$$x \geq -78.176760093132 \wedge x \leq -76.176760093132$$
$$x \geq -74.176760093132 \wedge x \leq -72.176760093132$$
$$x \geq -70.176760093132 \wedge x \leq -68.176760093132$$
$$x \geq -66.176760093132 \wedge x \leq -64.176760093132$$
$$x \geq -62.176760093132 \wedge x \leq -60.176760093132$$
$$x \geq -58.176760093132 \wedge x \leq -56.176760093132$$
$$x \geq -54.176760093132 \wedge x \leq -52.176760093132$$
$$x \geq -50.176760093132 \wedge x \leq -48.176760093132$$
$$x \geq -46.176760093132 \wedge x \leq -44.176760093132$$
$$x \geq -42.176760093132 \wedge x \leq -40.176760093132$$

Быстрый ответ

Данное неравенство не имеет решений

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