Question

logaritimo
log base é 0,2
$\sqrt[ \sqrt{3} ]{ \frac{1}{5} }$
​

Answer 1

Explicação passo-a-passo:

Log[0,2] (1/5^1/√3)

1/√3 log[2.10⁻¹] (5⁻¹)

-1/√3 log[2.10⁻¹] (5)             efetuando a mudança de base para 10

-1 ( log[10] (5)) / √3 ( log[10] (2.10⁻¹))

-1 (log[10] (5) ) / √3 ( log[10] (2) + log[10] (10⁻¹))

-1 (log[10] (5) ) / √3 ( log[10] (2) - log[10] (10))

-1 (log[10] (5) ) / √3 (log[10] (2) - 1)

-1 (log[10] (5) ) / √3 ( log[10] (10/5) - 1)

-1 (log[10] (5) ) / √3 ( log[10] (10) - log[10] (5) - 1 )

-1 (log[10] (5) ) / √3 (  1 - log[10](5) - 1)

-1 (log[10] (5) ) / √3 ( -log [10](5))

-log[10](5) / √3 ( -log [10](5))

Cortando o  -log [10](5)

1/√3

Racionalizando

1√3/ √3 . √3

√3/3

Acho q é isso