Question

qual o valor de x na questao ?

(5^x+1)+5^x+(5^x-1)= 775

Answer 1

Ola jsp

5^(x + 1) + 5^x + 5^(x - 1) = 775

5*5^x + 5^x + 5^x/5 = 775 

25*5^x + 5*5^x + 5^x = 5*775 

31*5^x = 3875 

5^x = 3875/31 = 125

5^x = 5^3

x = 3

Answer 2

Ae,

use as propriedades da exponenciação:


$\mathsf{5^{x+1}+5^x+5^{x-1}=775}\\ \mathsf{5^x\cdot5^1+5^x+5^x\cdot5^{-1}=775}\\\\ \mathsf{5\cdot5^x+5^x+ \dfrac{1}{5} \cdot5^x=775}\\\\ \mathsf{5^x~em~evidencia:}\\\\ \mathsf{5^x\cdot\left(5+1+ \dfrac{1}{5} \right)=775}\\\\ \mathsf{5^x\cdot\left( \dfrac{31}{5}\right)=775 }\\\\ \mathsf{5^x\cdot31=775\cdot5}\\ \mathsf{5^x\cdot31=3.875}\\\\ \mathsf{5^x= \dfrac{3.875}{31} }\\\\ \mathsf{5^x=125}\\ \mathsf{5^x=5^3}\\ \mathsf{\not5^x=\not5^3}\\\\ ~~~\mathsf{x=3}\\\\ \Large\boxed{\mathsf{S=\{3\}}}$

Tenha ótimos estudos ;P