Question

The luminosity of a star is 10 times, the luminosity of the Sun. Calculate the difference in their absolute magnitudes.

Answer 1

The difference is absolute magnitudes of two stars is given as follows (https://en.wikipedia.org/wiki/Luminosity#Relationship_to_magnitude):

$$\Delta M = -2.5\log_{10}\dfrac{L_1}{L_2}$$

where $\dfrac{L_1}{L_2 } = 10$ is the ratiof of the luminosities. Thus, obtain:

$$\Delta M = -2.5\log_{10}10 = -2.5$$

Answer. 2.5.