These two problems are nagging at me and I can't seem to piece together the correct resources to be able to answer them mathematically. These are homework questions, but I am not necessarily looking for answers; just techniques.
1) The star Capella is 14 pc away. The star Dubhe, the brightest star in the Big Dipper, is 160 pc away. Both stars have approximately equal luminosities. Which star appears brighter to us, and by what factor?
I know the nearer star will appear brighter, but I don't know how to quantify that notion.
2) Vega is a main sequence star, as is the Sun, but Vega has a luminosity about 50 times that of the Sun and a mass about 3.5 times that of the Sun. Which star will live longer, and by what factor?
I know the sun will live longer, but again, I don't know how to quantify it.
I didn't find the right solution from the Internet.