Binary star period calculation

[kdlsw]

The problem is attached, and the official answer is given.
The step in the answer does not make a lot of sense to me.
How does the luminosity L converted directly into distance d, and why is the solar distance is used?
And where does the dm=0.75 come from.
It's just not making sense to me...

Please expand and explain the steps in the answer a bit. Thank you.

 

[dauto]

m for the binary system is

m = -2.5log₁₀L + C

m' for a single star is

m' = -2.5log₁₀(L/2) + C
m' = -2.5[log₁₀L - log₁₀2] + C
m' = [-2.5log₁₀L + C] + 2.5log₁₀2
m' = m + 2.5log₁₀2 = m + δm

δm = 2.5log₁₀2 = 0.752575... ≈ 0.75

 

[dauto]

The relation between magnitude and distance comes from the inverse square law for the radiation intensity. If you double the distance to a star than its radiation intensity drops to (1/2)² = 1/4 and so forth so if you know the apparent magnitude you can figure the distance.