Question 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 $k + a + b?$