Question 1209372
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<pre>

    {{{3^0}}} = 1,

    {{{3^1}}} = 3,

    {{{3^2}}} = 9,

    {{{3^3}}} = 27,

    {{{3^4}}} = 81,

    {{{3^5}}} = 243.


At this point, it should be clear that there is no need to consider degrees higher than {{{3^4}}} = 81.


Trial and error method gives two solutions

    27 + 81 = 108,   81 + 27 = 108,

that are

    {{{3^3}}} + {{{3^4}}} = 108,  {{{3^4}}} + {{{3^3}}} = 108.


So, possible pairs (x,y) are  (3,4)  and  (4,3).    <U>ANSWER</U>
</pre>

Solved.



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Commenting Edwin's post, the "trial and error" is the method which children learn intuitively 
at the kindergarten age before they come to school and before they start learning Math.