Em um arquivo de configuração da web, eu faria o seguinte:

<entityFramework>
<defaultConnectionFactory type="System.Data.Entity.Infrastructure.SqlConnectionFactory, EntityFramework" />
<providers>
  <provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
</providers>

<interceptors>
  <interceptor type="System.Data.Entity.Infrastructure.Interception.DatabaseLogger, EntityFramework">
    <parameters>
      <parameter value="C:\tmp\DataAccessLogOutput.txt" />
    </parameters>
  </interceptor>
</interceptors>
</entityFramework>

Mas como faço isso no config.json do vnext:

{
    "Data": {
        "DefaultConnection": { 
            "ConnectionString": "Server=(localdb)\\mssqllocaldb;Database=aspnet5-Cupcake-a652ca1c-0d92-4155-ad46-bfb68bb538ee;Trusted_Connection=True;MultipleActiveResultSets=true"
        }
    },
    "EntityFramework": {
        "ApplicationDbContext": {
            "ConnectionStringKey": "Data:DefaultConnection:ConnectionString",
        }
    }
}