Question

Resolva a equação exponencial:

Answer 1

Ótima questão, vamos lá achar a solução.


$[(0,2)^{3/4}]^{x/2} = \sqrt[5]{( \frac{1}{5})^{1/4} } \\\\ ( \frac{1}{5} )^{3x/8} = [( \frac{1}{5}^{1/4})]^{1/5} \\\\ ( \frac{1}{5} )^{3x/8} = ( \frac{1}{5} )^{1/20}\\\\ \frac{3x}{8} = \frac{1}{20} \\\\ 3x*20=8\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{\boxed{\boxed{x=2/15}}$

Answer 2

     [( 0,2)]^3x/8 = (1/5)^4/5 ------>  (2/10)^3x/8 = (1/5)^4/5-------> como 2/10 =

1/5 temos  (1/5)^3x/8  =  (1/5)^5/5 -------> bases iguais, expoentes iguais --------

-------->  3x/8 = 4/5 ----->  5.3x = 4.8 -----> 15x = 32 ----> x = 32/15

  S = { 32/15}  tá aí ok?