Question

${3}^{x - 1} - {3}^{x} + {3}^{x + 2} = 306$
​

Answer 1

Resposta:

x= 3 + (log 17 + 3.log 2 - 2)/log 3

ou

x~ 3,279

Explicação passo-a-passo:

Temos que:

3^(x - 1) - 3^x + 3^(x + 2) = 306

(3^x)/3 - 3^x + (3^x). (3^2) = 306

[ (3^x) - (3^x).3 + (3^x). (3^2).3 ] /3 = 306

(3^x) - 3.(3^x) + 27.(3^x) = 306. 3

25.(3^x) = 918

3^x = 918/25

3^x = (3^3).34/25

log 3^x = log (3^3).34/25

x.log 3 = 3.log 3 + log 34 - log 25

x.log 3 = 3.log 3 + log 17.2 - log 5^2

x.log 3 = 3.log 3 + log 17 + log 2 - 2.log 5

x.log 3 = 3.log 3 + log 17 + log 2 - 2.log 10/2

x.log 3 = 3.log 3 + log 17 + log 2 - 2.(log 10 - log 2)

x.log 3 = 3.log 3 + log 17 + log 2 - 2.(1 - log 2)

x.log 3 = 3.log 3 + log 17 + log 2 - 2 + 2.log 2

x.log 3 = 3.log 3 + log 17 + 3.log 2 - 2

x= (3.log 3 + log 17 + 3.log 2 - 2)/log 3

x= 3 + (log 17 + 3.log 2 - 2)/log 3

x~ 3,279

Blz?

Abs :)