Using Brightness=Lumnosity/Distance^2 ............Help this is so hard!?

Question

A star has an observer brightness of 0.01 Lumnosity. And temp. of 10,000K, how far away is this star (this will give you distance as multiple of the Earth-sun radii)?

Temp. 2.9*10^6/PeakWL

Answer 1

You're not stating the question clearly and there's not enough information. Luminosity is a property of the star that doesn't depend on observer distance while brightness does. Is 0.01 the observed brightness relative to the sun? Or a known luminosity relative to the sun? Restate your question. The answer will be complicated by the fact that the star's temperature is higher than the sun's (which is given as 5785 K). If "Temp. 2.9*10^6/peak WL" is significant you should explain what it is.
Here is a very partial answer. If the star is a sun-like body with the same luminosity as the sun and we disregard the temperature difference, and 0.01 is the sun-relative observed brightness, the star is 10 earth-sun radii from us due to the simple inverse-square relation of brightness = luminosity / distance^2 you mentioned in the question.