a) x = 1
b) x = 1
c) x = 0
Explicação passo-a-passo:
a)
[tex] {( \frac{5}{3} )}^{3x - 1} = \frac{25}{9} \\ {( \frac{5}{3} )}^{3x - 1} = {( \frac{5}{3} )}^{2} \\ 3x - 1 = 2 \\ 3x = 2 + 1 \\ x = \frac{3}{3} = 1[/tex]
b)
[tex] {( \frac{8}{27} )}^{2x} = \frac{64}{729} \\ {( \frac{ {2}^{3} }{ {3}^{3} } )}^{2x} = \frac{ {2}^{6} }{ {3}^{6} } \\ {( \frac{2}{3} )}^{2x \times 3} = {( \frac{2}{3} )}^{6} \\ 6x = 6 \\ x = \frac{6}{6} = 1[/tex]
c)
[tex] {( \frac{1}{1024} )}^{ \frac{x}{2} } = 1 \\ {( \frac{ {1}^{10} }{ {2}^{10} } )}^{ \frac{x}{2} } = 1 \\ {( \frac{1}{2} )}^{10 \times \frac{x}{2} } = {( \frac{1}{2} )}^{0} \\ \frac{10x}{2} = 0 \\ x = 0[/tex]
