(log3 2+log9 2)*(log4 3+log8 3)
=(log3 2+log(3)^2 2)*(log(2)^2 3 +log(2)^3 3)
=(log3 2+1/2 *log3 2)*(1/2*log2 3 +1/3*log2 3)
=3/2*(log3 2)*5/6 *(log2 3)
=5/4
(log3 2+log9 2)*(log4 3+log8 3)
=(log3 2+log(3)^2 2)*(log(2)^2 3 +log(2)^3 3)
=(log3 2+1/2 *log3 2)*(1/2*log2 3 +1/3*log2 3)
=3/2*(log3 2)*5/6 *(log2 3)
=5/4