Question

Resolva as seguintes equações exponenciais: a)9^x-2=raiz de 27 b)5^2x-1=1 c)2/5^x-1=125/8

Answer 1

A                                              

9^(x-2) = 27^1/2                          

2x -1 = 0

2x = 1

x = 1/2                

B

3^2*(x-2) = 3^3*1/2  

2x-4 = 3/2  

2x = 3/2 + 8/2  

2x = 11/2  

x = 11/4

C

(\frac{2}{5})^{x-1}=\frac{125}{8} >>(\frac{2}{5})^{x-1}=\frac{5^3}{2^3}>>(\frac{2}{5})^{x-1}=(\frac{5}{2})^3

Igualando as bases:

(\frac{2}{5})^{(x-1)^{-1}}=(\frac{5}{2})^{3^{-1}}>>(\frac{2}{5})^{-x+1}=(\frac{5}{2})^{-3}>>(\frac{2}{5})^{-x+1}=(\frac{2}{5})^{3}

Bases iguais expoêntes iguais:

-x+1=3

-x=2

x=-2