Question

Equação Exponencial:
2^x+1 + 2^x-2 = 9/2

Answer 1

Resposta:

2^(x+1) + 2^(x-2)= 9/2

2 * 2^(x) +2⁻²*2^(x) =9/2

2^(x) *(2+1/2²) =9/2

2^(x) * (8+1)/4=9/2

2^(x)=2

2^(x) = 2¹

x=1

Answer 2

Resposta:

x=1

Explicação passo-a-passo:

$\displaystyle 2^{(x+1)}+2^{(x-2)}=\frac{9}{2}\\\\2^{x}.2^{1}+2^{x}2^{-2}=\frac{9}{2}\\\\2^{x}.2+\frac{2^{x}}{2^{2}}=\frac{9}{2}\\\\2^{x}.2+\frac{2^{x}}{4}=\frac{9}{2}\\\\\frac{2^{x}.4.2+2^{x}}{4}=\frac{9}{2}\\\\\frac{2^{x}.8+2^{x}}{4}=\frac{9}{2}\\\\\frac{2^{x}.9}{4}=\frac{9}{2}\\\\2^{x}=2\\\\2^{x}=2^{1}\\\\x=1$

Propriedades:  

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$