Question

The total luminosity at all wavelengths of the magnetar burst observed on December 27,2006 was approximately 10^14 Lum. At what distance from the magnetar would the brightness of the burst have been equal to the brightness of the Sun as seen on Earth?

Answer 1

You can find the distance where brightness of the burst have been equal to the brightness of the Sun as seen on Earth in following way:
Distance to the Sun * square root of (Luminosity/Luminosity of the Sun)
Luminosity is given in the problem and approximately equal to 10^14Lum.