Question

O valor de x para que se tenha f(x) = 131 é?

a) Nenhuma das alternativas
b) 5
c) 2
d) 4
e) 3

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{f(x) = 5^{x - 2} + 5^{x + 1} + 5^{x - 1}}$

$\mathsf{5^{x - 2} + 5^{x + 1} + 5^{x - 1} = 131}$

$\mathsf{5^x.5^{-2} + 5^x.5 + 5^x.5^{-1} = 131}$

$\mathsf{5^x(5^{-2} + 5 + 5^{-1}) = 131}$

$\mathsf{5^x\left(\left(\dfrac{1}{5}\right)^2 + \left(\dfrac{5}{1}\right) + \left(\dfrac{1}{5}\right)\right) = 131}$

$\mathsf{5^x\left(\left(\dfrac{1}{25}\right) + \left(\dfrac{5}{1}\right) + \left(\dfrac{1}{5}\right)\right) = 131}$

$\mathsf{5^x\left(\dfrac{1 + 125 + 5}{25}\right) = 131}$

$\mathsf{5^x\left(\dfrac{\not1\not3\not1}{25}\right) = \not1\not3\not1}$

$\mathsf{5^x = 25}$

$\mathsf{\not5^x = \not5^2}$

$\boxed{\boxed{\mathsf{x = 2}}}\leftarrow\textsf{letra C}$