How can you find the age of a star based on the luminosity?

Answer 1

The more luminous the star the faster it uses up its nuclear fuel and dies, but you cannot tell how much of its lifetime it has used up just by knowing its luminosity, you can only say it is not older than the lifetime of stars of that luminosity.

Answer 2

You cannot do it based on the luminosity alone. The luminosity increases with the 4th power of the temperature and the square of the radius, so a cool, large star (which is usually an old star) can have the same total luminosity as a hot, smaller one (which is usually a young star). You *can* do it with a combination of luminosity and color (or spectrum), which enables you to distinguish between those two cases. A hotter (thus younger) star will have a bluer spectrum then a cool, old giant star.