Solve the equation. $$ \left(\frac{2}{5}\right)^{\mathrm{x}}=\left(\frac{8}{125}\right) $$ The solution set is $$ \{\square\} $$. Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

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1. Write the equation:
   $$
   \left(\frac{2}{5}\right)^x = \frac{8}{125}
   $$

2. Express the right side as a power of $$\frac{2}{5}$$. Notice that:
   $$
   \frac{8}{125} = \frac{2^3}{5^3} = \left(\frac{2}{5}\right)^3
   $$

3. Now the equation becomes:
   $$
   \left(\frac{2}{5}\right)^x = \left(\frac{2}{5}\right)^3
   $$

4. Since the bases are the same, equate the exponents:
   $$
   x = 3
   $$

Thus, the solution set is $$\{3\}$$.
The solution is $$ x = 3 $$.

Solve the equation.

The solution set is .
Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

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Solve the equation. The solution set is . Type an integer or a simplified fraction. Use a comma to separate answers as needed.)