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taylortuanquin
You don't mention if you want the ratio X:Y or Y:X. 

Apparent magnitude was originally based on how bright something appeared to the eye such that a star that is half as bright had one higher magnitude. The visible stars were divided into magnitudes 1 to 6 with the brightest being 1 and the dimmest being 6. This was later formalized into a more scientific definition where a magnitude 1 star was said to be 100x brighter than a magnitude 6 stars. Thus a change of 5 magnitudes represents 100 times difference in brightness or a change of one magnitude is a change in brightness by a factor of the fifth root of 100. This fifth root of 100 is called Pogson's ratio. It is approximately 2.51. So a change in magnitude from 10 to 13 means it is three orders of magnitude dimmer and therefore 1/2.51^3 = 1/15.8th as bright. 

So your answer is either 15.8 : 1 or 1 : 15.8 depending on whether you want the ratio of y : x or x : y. 

Note star x is the one that is 15.8 times dimmer than star y.
samuelonum1

Answer:

star y is brighter than star x

Explanation:

Actually the brightness of a star is seen in its magnitude, the lower the magnitude the brighter the star, and Also the larger the magnitude the dimmer the star

To calculate the difference in magnitude

Star x has a magnitude of 13

Star y has a magnitude of 10

The difference in magnitude is

13-10= 3

Hence star y is brighter than star x

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