Question

o valor de x que torna verdadeira a equação

2^x . 4^x+1 . 8^x+2 = 16^x+3 é: (PRA HJ PFV)

Answer 1

Resposta:

x=2

Explicação passo-a-passo:

4=2.2=2²

8=2.2.2=2³

16=2.2.2.2=2⁴

$\displaystyle\\2^x.4^{(x+1)}.8^{(x+2)}=16^{(x+3)}\\\\2^x.2^2^{(x+1)}.2^3^{(x+2)}=2^4^{(x+3)}\\\\2^{x+2(x+1)+3(x+2)}}=2^4^{(x+3)}$

As bases são iguais, então:

x+2(x+1)+3(x+2)=4(x+3)

x+2x+2+3x+6=4x+12

6x+8=4x+12

6x-4x=12-8

2x=4

x=4/2

x=2

Propriedades:

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