This paper is concerned with the analysis of the equation
x
y
=
y
z
{x^y} = {y^z}
, where
x
,
y
,
z
x,y,z
are variables ranging over ordinals, and where both sides of the equation are transfinite in value. The method used for this analysis consists in regarding
y
y
as a parameter and
x
x
as an independent variable, and determining necessary and sufficient conditions to be placed upon
x
x
so that the resulting equation in
z
z
has a solution. Extensive use is made of normal form, as well as results in ordinal arithmetic by both Bachmann and Sherman.