To solve the equation [tex]\( 5^{5x} = 25 \)[/tex]:
1. Recognize the relationship between bases and exponents:
- The base on the left-hand side of the equation is 5, and 25 can be expressed as a power of 5.
- Note that [tex]\( 25 = 5^2 \)[/tex].
2. Rewrite the equation using the same base:
[tex]\[
5^{5x} = 5^2
\][/tex]
3. Equate the exponents (since the bases are the same, the exponents must be equal):
[tex]\[
5x = 2
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{2}{5}
\][/tex]
Thus, the solution is:
[tex]\[
\boxed{\frac{2}{5}}
\][/tex]
So, the correct answer is:
A. The solution is [tex]\( x = \frac{2}{5} \)[/tex].
