Question

${4}^{x} - {3}^{x - \frac{1}{2} } = {3}^{x + \frac{1}{2} } - {2}^{2x - 1}$
Quero ver a resolução completa.​

Answer 1

Resposta:

(2²)^(x) -3^(x-1/2)=3^(x+1/2)-2^(2x-1)

2^(2x)-3^(x) *3^(-1/2) =3^(x) * 3^(1/2) -2^(2x)*2^(-1)

2^(2x)*[1+2^(-1)] =3^(x) *[3^(-1/2) +3^(1/2)]

2^(2x)*[1+1/2] =3^(x) *[1/√3 +√3]

2^(2x)*[3/2] =3^(x) *[1 +√3²]/√3

2^(2x)*[3/2] =3^(x) *[1 +3]/√3

2^(2x)*[3/2] =3^(x) *[4]/√3

2^(2x)=3^(x) * 8/(3√3)

2^(2x-3) =3^(x)/(3^(3/2)

2^(2x-3) =3^(x-3/2)

2^[2*(x-3/2)] =3^(x-3/2)

4^(x-3/2) =3^(x-3/2)

só será verdadeiro para x-3/2=0   ==>x=3/2