Question 1148535
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<pre>

If  {{{a^b}}} = {{{b^a}}}  and  b = 9a,  then


    {{{a^(9a)}}} = {{{(9a)^a}}},


    {{{(a^9)^a}}} = {{{(9a)^a}}};


        then, since indexes on the left and on the right are equal, the bases  {{{a^9}}}  and  {{{9a}}}  must be equal too,  which gives

    {{{a^9}}} = 9a.


It gives

    {{{a^8}}} = 9.

which implies

    a = {{{root(8,9)}}} = {{{root(4,3)}}}.    <U>ANSWER</U>
</pre>

Solved and completed.