Answer:
The solution is [tex]x = -\frac{5}{6}[/tex]
Step-by-step explanation:
We solve this question using exponential properties.
We have that:
[tex](\frac{25}{4})^{3x} = \frac{32}{3125}[/tex]
Simplifying:
[tex](\frac{5^2}{2^2})^{3x} = \frac{2^5}{5^5}[/tex]
[tex]([\frac{5}{2}]^{2})^{3x} = (\frac{2}{5})^{5}[/tex]
[tex](\frac{5}{2})^{6x} = (\frac{2}{5})^{5}[/tex]
Changing the numerator and denominator in the right side:
[tex](\frac{5}{2})^{6x} = (\frac{5}{2})^{-5}[/tex]
Since both bases are equal:
[tex]6x = -5[/tex]
[tex]x = -\frac{5}{6}[/tex]
The solution is [tex]x = -\frac{5}{6}[/tex]
