Question 84325
Take log (base 10) of both sides.
{{{log(2^(log 3*3^(1/2)))=log(3^(k*log (2)))}}}
{{{log(3^(3/2))*log(2)=k*log(2)*log(3)}}}
{{{(3/2)*log(3)*log(2)=k*log(2)*log(3)}}}
This give {{{k=3/2}}}