Answer:
x = 17/7
Step-by-step explanation:
Given-
[tex](\frac{5}{3} )^{x - 8}[/tex] = [tex]( \frac{27}{125} ) ^{2 x - 3}[/tex]
[tex](\frac{5}{3} )^{x - 8}[/tex] = [tex]((\frac{3}{5} ) ^{3}) ^{2 x - 3}[/tex]
[tex](\frac{5}{3} )^{x - 8}[/tex] = [tex](( \frac{5}{3} ) ^{(-3)})^{2 x - 3}[/tex]
[tex](\frac{5}{3} )^{x - 8}[/tex] = [tex](\frac{5}{3} )^{ - 6 x + 9}[/tex]
On comparing both sides-
x - 8 = - 6 x + 9
7 x = 17
x = 17/7
∴ x = 17/7.
