Răspuns:
Explicație pas cu pas:
2^2019+2^2020+2^2021 = 2^2019*(1 + 2 + 2^2) = 7*2^2019
32^404 = (2^5)^404 = 2^2020
0,5 = 5/10 = 1/2
2^2020/(1/2) = 2^2020*2/1 = 2^2021
7*2^2019/x = 2^2021
x = 7*2^2019/2^2021 = 7/2^2 = 7/4
Răspuns:
[tex]x = \frac{7}{4} \\ [/tex]
Explicație pas cu pas:
[tex] \frac{ {2}^{2019} + {2}^{2020} + {2}^{2021} }{x} = \frac{ {32}^{404} }{0,5} \: , \: x \neq 0\\ [/tex]
[tex] \frac{2 {}^{2019}(1 + 2 + {2}^{2} )}{x} = \frac{(2 {}^{5} ) {}^{404} }{ \frac{1}{2} } \\ [/tex]
[tex] \frac{ {2}^{2019}(1 + 2 + 4) }{x} = 2^{2020} \cdot 2 \\ [/tex]
[tex] \frac{ {2}^{2019} \cdot7}{x} = {2}^{2021} \\ [/tex]
[tex] {2}^{2019} \cdot 7 = {2}^{2021} \cdot x[/tex]
[tex] {2}^{2021} \cdot x = 7 \cdot {2}^{2019} [/tex]
[tex] x = \frac{7 \cdot {2}^{2019} }{ {2}^{2021} } = \frac{7}{ {2}^{2} } = \boxed{ \frac{7}{4}} \\ [/tex]
