2025 AMC 12A Problem 7

In a certain alien world, the maximum running speed v of an organism is dependent on its number of toes n and number of eyes m. The relationship can be expressed as v = k n^a m^b centimeters per hour, where k, a, and b are integer constants. In a population where all organisms have 5 toes, \log v = 4 + 2\log m; and in a population where all organisms have 25 eyes, \log v = 4 + 4\log n, where the logarithms are base 10. What is k + a + b?

\textbf{(A)} 20 \qquad \textbf{(B)} 21 \qquad \textbf{(C)} 22 \qquad \textbf{(D)} 23 \qquad \textbf{(E)} 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.