how many times brighter is a first magnitude star than a third magnitude star
Magnitude (astronomy) The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly a hundred times brighter than a magnitude 6 star, as the difference of five magnitude steps corresponds to 2.5125, or 100.