Question 1065452
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Prove that {{{ a^b = b^a }}} with a= 2 1/4 and b= 3 3/8.
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Notice that a = {{{9/4}}}  and b = {{{27/8}}}.


Take logarithms of both sides.


<pre>
{{{log((a^b))}}} = {{{b*log((a))}}} = {{{(27/8)*log((9/4))}}} = {{{27/8)*log(((3/2))^2)}}} = {{{(27/8)*2*log((3/2))}}} = {{{(27/4)*log((3/2))}}}.


{{{log((b^a))}}} = {{{a*log((b))}}} = {{{(9/4)*log((27/8))}}} = {{{9/4)*log(((3/2))^3)}}} = {{{(9/4)*3*log((3/2))}}} = {{{(27/4)*log((3/2))}}}.


We just got that the logarithms are the same.


Hence, the under-the-logarithm expressions are equal.
</pre>

Proved and solved.