Wouldn't it be great if you could get the first element of an array in O(logn) ? Well in Ruby you can with .index... but if you couldn't, here's what I'd do.

array_first_index.rb

class Array

  def first_index(x)
    key = x
    f = 0
    b = self.size
    mid = get_mid(f,b)

    until f == (b - 1) || f == b
      self[mid] < key ? f = mid : b = mid
      mid = get_mid(f,b)
    end
    if self[f] == key
      f
    elsif self[b] == key
      b
    else
      nil
    end
  end

  def get_mid(front,back)
    middle = ((back - front) / 2) + front
  end
end