First off I will provide the rules for brothels as:
1. They require condoms.
2. They accept any customer.
3. They must prove they are free of STDs regularly. (monthly)
4. Each person has their own prices and list of what they are willing to do.

In 2003 Rhode Island, accidentally decriminalized prostitution. The effects of this were “caused both forcible rape offenses and gonorrhea incidence to decline for the overall population. Our synthetic control model finds 824 fewer reported rape offenses (31 percent decrease) and 1,035 fewer cases of female gonorrhea (39 percent decrease) from 2004 to 2009”
http://www.nber.org/papers/w20281

This breaks down into two argument in favor of legalized prostitution.

1) Rape dropped by 824. The effects of which will affect the victim for the rest of their lives.
https://mainweb-v.musc.edu/vawprevention/research/mentalimpact.shtml

2) Gonorrhea dropped by 1,035. STDs are a critical health concern affecting this country.
https://www.health.ny.gov/publications/3805.pdf

3) It is hypocrisy with prostitution being illegal, while porn is legal. Whatever argument can be for or against, one can be made for the other.
http://www.cnn.com/2005/LAW/08/12/colb.pornography/index.html?iref=allse...

4) No one sees any problem with massages. No one sees any problem getting their hair, nails, or feet done. In all these cases, you are paying another human being to touch you. How is sex any different?

5) Freedom is being able to choose what you do with your body. Choosing to have sex with someone for money is no different.