Question

$\sqrt{( \frac{4}{9} } ) {}^{x} = 0.6$
alguém me ajuda, como faz isso?​

Answer 1

Resposta:

x~ 1,26

Explicação passo-a-passo:

Temos que:

raiz((4/9)^x)= 0,6

[raiz((4/9)^x)]^2 = [6/10]^2

(4/9)^x = (3/5)^2

log (4/9)^x = log (3/5)^2

x. log 4/9 = 2. log 3/5

x. (log 4 - log 9) = 2. (log 3 - log 5)

x. (log 2^2 - log 3^2) = 2. (log 3 - log 5)

x. (2.log 2 - 2.log 3) = 2. (log 3 - log 5)

x. 2. (log 2 - log 3) = 2. (log 3 - log 5)

x. (log 2 - log 3) = (log 3 - log 5)

x = (log 3 - log 5) / (log 2 - log 3)

x = (log 5 - log 3) / (log 3 - log 2)

x = (log 10/2 - log 3) / (log 3 - log 2)

x = (log 10 - log 2 - log 3) / (log 3 - log 2)

x = (1 - log 2 - log 3) / (log 3 - log 2)

x = [1 - (log 3 + log 2)] / (log 3 - log 2)

Sendo:

log 2~ 0,301

log 3~ 0,477

Temos:

x = [1 - (0,477 + 0,301)] / (0,477 - 0,301)

x= (1 - 0,778) / 0,176

x= 0,222 / 0,176

x~ 1,26

Blz?

Abs :)