For a non-constant entire function f(z) — z —r e’0, the logarithmic order p* (1 < -p* < 00) and lower logaritghmic order X* (1 < X* < 00 ) are given by thelimit superior and limit inferior of {log log M(r)| /(log log r), asr—>■ 00, respectively, where M(r) —: max j f(z) In this paper we derive a formula for X*—type t?k* Hm inf(log M(r)/(lo