Evaluate 25^{log_5 4}.

Introduction / Context:
Powers of logs often simplify via base-matching identities. Here 25 is a power of 5, and the exponent involves log base 5, which suggests rewriting to use a^log_a(b) = b.

Given Data / Assumptions:
Compute 25^{log_5 4}, noting 25 = 5^2.

Concept / Approach:
Use exponent rules: (5^2)^{log_5 4} = 5^{2 * log_5 4}. Then apply the identity 5^{log_5 4} = 4 to simplify.

Step-by-Step Solution:

Verification / Alternative check:
Numerically, log_5 4 ≈ 0.861... Then 25^{0.861...} ≈ 16 ✓.

Why Other Options Are Wrong:
5 or 25 result from misapplying a^log_a(b) = b or forgetting the outer square.

Common Pitfalls:
Applying log identity directly to 25 rather than rewriting it as 5^2 first.

Final Answer:
16