config.ru

require 'my_app'

MyApp.set :logger, MyFancyLogger.new

run MyApp

logger_demo.rb

require 'sinatra/base'

class MyApp < Sinatra::Base
  get '/' do
    # Note: I'm not sure if you can access the logger directly, but it'd be trivial to add a helper method that allows that
    logger.info "Serving /…"
  end
end