Question

Determine a raiz da função exponencial abaixo:

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

Answer 1

Oie, Td Bom?!

$f(x) = 5 {}^{x + 1} + 5 {}^{x} + 5 {}^{x - 1} - 775$

>>> Substitua: f(x) = 0.

$0 = 5 {}^{x + 1} + 5 {}^{x} + 5 {}^{x - 1} - 775$

$775 = 5 {}^{x + 1} + 5 {}^{x} + 5 {}^{x - 1}$

$775 = (5 {}^{2} + 5 + 1).5 {}^{x - 1}$

$775 = (25 + 5 + 1).5 {}^{x - 1}$

$775 = 31.5 {}^{x - 1}$

$31.5 {}^{x - 1} = 775$

$5 {}^{x - 1} = 25$

$5 {}^{x - 1} = 5 {}^{2}$

$x - 1 = 2$

$x = 2 + 1$

$x = 3$

Att. Makaveli1996