Find how long a beam of light emitted at a certain time takes to reach

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To determine when the first light from galaxy X reaches our galaxy, the proper distance at the time of emission (10 million light-years) and the Hubble constant need to be considered. The light emitted at time t = tH/1000 (14 million years ago) must be analyzed using Hubble's law, which describes the relationship between distance and the rate of expansion of the universe. The solution involves integrating the equations provided, specifically focusing on the exponential relationship of distance over time. Clarification is needed on how the additional equations relate to the problem at hand. The goal is to calculate the time it takes for the light beam to travel from galaxy X to Earth.
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Homework Statement

3. In the model of “Empty Universe” consider a galaxy X, which starts emitting light at time t = tH/1000 (14 My). If, at that time, the proper distance between “X” and our galaxy was 10 Mly at what time the first light from “X” is expected to arrive to our galaxy?



Homework Equations



V=HD
Lp=Cth*ln(z+1)/z

Lp is proper length at time emitted and Cth is Hubble length.


The Attempt at a Solution



I'm pretty sure I just need to find how long it takes for the light beam to reach Earth from galaxy X. To do that I just integrate the Hubbles law equation and get this exponential for D which is De^(Ht) then set it equal to x=ct where c is speed of light. However I'm being given equations for other things and I don;t know how they are relevant to this problem.
 
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