Implementing addition using multiplication
<p>I've been familiar with the famous question of implementing multiplication using addition, or exponentiation using multiplication, using algorithms of looping or bit-shifting and adding shifted bit groups combos.</p>

<p>Now, I wondered if there is any way to implement addition using only higher level operations, such as multiplication specifically, or exponentiation, logarithm etc. (subtraction excluded)</p>

<p>Can this be achieved with some algorithm combining these operations (and possibly bitwise operators as assistants) or is addition a fundamental operation that serves as an axiom, so it can't be reproduced in other ways except for its definition?</p>

<p>Thanks.</p>