Задача 53212 5*(1/2)^(x-3)+(1/2)^(x+1) = 162...

5f58ae0794ec612a7a933adc

09.09.2020 13:30:26

5*(1/2)^(x-3)+(1/2)^(x+1) = 162

5f3ea7e3faf909182968ddd9

09.09.2020 13:47:09

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Выносим за скобки [m] \frac{1}{2}[/m] в меньшей степени:

[m] (\frac{1}{2})^{x-3}\cdot (5 +(\frac{1}{2})^{x+1-(x-3)})=162[/m]

При делении [m] (\frac{1}{2})^{x+1}[/m] на [m] (\frac{1}{2})^{x-3}[/m] показатели вычитаются


[m] (\frac{1}{2})^{x-3}\cdot (5 +(\frac{1}{2})^{4})=162[/m]

[m] (\frac{1}{2})^{x-3}\cdot (5 +\frac{1}{16})=162[/m]

[m] (\frac{1}{2})^{x-3}\cdot \frac{81}{16}=162[/m]

[m] (\frac{1}{2})^{x-3}=32[/m]

[m] (\frac{1}{2})^{x-3}=(\frac{1}{2})^{-5}[/m]

[m] x-3=-5[/m]

[m]x=-2[/m]

О т в е т. -2