Deciding the Most Significant Bit of Binary Multiplication
Multiplication is complete for $\mathsf{TC}^0$ and 
this is a well know result. 
The reduction is from Count 
(number of 1 bits in a binary number). 
Comparison of binary numbers is in $\mathsf{AC^0}$ 
so $\mathsf{Majority}$ is reducible to $\mathsf{Count}$. 

To reduce $\mathsf{Count}$ to $\mathsf{Mult}$ do as follows: 
consider input is $a_0a_1\ldots a_n$. 
Insert $k$ 0s between $a_i$s and call it $a$. 
Multiply it with $b$ which is like $a$ except that 
$a_i$s in it are replaced with 1s. 
Pick $k&gt;3n$. 
The number in the middle section of $ab$ is the answer. 
The reduction is in $\mathsf{FO}$ and shows that 
$\mathsf{Count} \in \mathsf{FO(Mult)}$.