(log3^4+log5^2)(log2^9+log2^根号3)
=(lg4/lg3+lg2/lg5)(lg9/lg2+lg根号3/lg2)
=(2lg2*lg5+lg2*lg3)/lg3*lg5*(lg9+lg根号3)/lg2
=3/2(2lg5+lg3)/lg5
=3/2lg(25/3)/lg5
=3/2log5^(25/3)