global

def log_with_optional_base(numeric, base = Backports::Undefined)
  if base.equal?(Backports::Undefined)
    # Math.log(n) in 1.9.1 no longer accepts string arguments as it
    # did on 1.8.x, but we won't risk redefining existing behavior
    # when called with just one argument.
    log_without_optional_base(numeric)
  else
    # Math.log(n, b) in 1.9.1 does not accept string arguments:
    raise TypeError, "can't convert String into Float" if numeric.is_a?(String) || base.is_a?(String)
    log_without_optional_base(numeric) / log_without_optional_base(base)
  end
end