Question

Determine o conjunto verdade.
Me ajudem por favor
$2 {}^{x + 2} + 2 {}^{x - 1 } = 18$
$2 {}^{x + 1} + 2 {}^{x + 3} = 20$
$5 {}^{x - 2} + 5 {}^{x + 1} = 126$

Answer 1

$2^{x+2}+2^{x-1}=18 \\ \\ 2^x(2^2+2^{-1})=18 \\ \\ 2^x(4+\frac{1}{2})=18 \\ \\ 2^x\cdot\frac{9}{2}=18 \\ \\ 2^x=18\cdot\frac{2}{9} \\ \\ 2^x=4 \\ \\ 2^x=2^2 \\ \\ x=2$

$2^{x+1}+2^{x+3}=20 \\ \\ 2^x(2+2^3)=20 \\ \\ 2^x(2+8)=20 \\ \\ 2^x\cdot10=20 \\ \\ 2^x=\frac{20}{10} \\ \\ 2^x=2 \\ \\ x=1$

$5^{x-2}+5^{x+1}=126 \\ \\ 5^x(5^{-2}+5)=126 \\ \\ 5^x(\frac{1}{25}+5)=126 \\ \\ 5^x\cdot\frac{126}{25}=126 \\ \\ 5^x=126\cdot\frac{25}{126} \\ \\ 5^x=25 \\ \\ 5^x=5^2 \\ \\ x=2$