Question

Log de raiz cúbica de 2 sobre 2 na base 4

Answer 1

Vejamos:

log (∛2)/2   =   x
     4
      
* Aplicando a Definição:

(∛2)/2    =    4^x

∛2               4^x
------   =   
  2

∛2               [(2)^2]^x
------   =   
  2

2^1/3          [(2)^2]^x
--------   =
    2

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

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

2^(-2/3) = 2^2x


(-2/3) = 2x
2x = -2/3
x = -2/3/2
x = -2/3 . 1/2
x =  -2/6
x = -1/3

Answer 2

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}log_4\ (\frac{\sqrt[3]{2}}{2}) = x\\\\4^x = \frac{\sqrt[3]{2}}{2}\\\\2^{2x} = \frac{2^{\frac{1}{3}}}{2}\\\\2^{2x} = 2^{\frac{1}{3}-1}\\\\2^{2x} = 2^{-\frac{2}{3}}\\\\2x = -\frac{2}{3}\\\\6x = -2\\\\\boxed{\boxed{x = -\frac{2}{6} = -\frac{1}{3}}}\end{array}\right$

Espero ter ajudado. =^.^=