Question

Qual é o log de 2 raiz quadrada de 8 na base 1/4?

Answer 1

Resposta:

log 2√8 = x

    1/4

(1/4)^x = 2.√4.2

(1/4)^x = 2.2.√2

(1/4)^x = 4.√2

(1/4)^x = 4.2^1/2

(1/4)^x = (2^2).(2^1/2)

(1/4)^x = 2^(2 + 1/2)                    2 + 1/2 = (4 + 1)/2 = 5/2

(1/4)^x = 2^5/2

4^-x = 2^5/2

(2^2)^ -x = 2^5/2

2^-2x = 2^5/2

-2x = 5/2 (-1)

2x = -5/2

x = (-5/2)/2

x = -5/2.2

x = -5/4

Explicação passo-a-passo: