Subtracting a number relates to summing a number, as dividing by a number relates to multiplying by a number, as ??? relates to powering by a number.
May I put it in a more mathematical manner:
$x-y \leftrightarrow x+y\space; \space\space\space\frac{x}{y} \leftrightarrow xy\space ; \space\space\space???\leftrightarrow x^y$
where$\space\space"\leftrightarrow "\space\space$represents a relationship between its sides.
Who is $\space$"???"$\space$ ?
I realise that there are actually two questions here: who is question marks and what is the relation to be considered.
(numbers are over the $\mathbb{R}$ field)
At first it seemed intuitive for me to set $\space\space ???\space\space =\space\space \log_{y}x \space\space\space$;
but then I could find no words to describe the relationship $\space"\leftrightarrow "\space$ which justifies that choice.
All the pairs of operations you mention are called "inverse operations" - you use one to undo the other. For example, if you wanted to solve an equation that involved subtraction, you would use addition: $$x-3=0$$ $$x-3\color{red}{+3}=0\color{red}{+3}$$ $$x=3$$ The same is true for multiplication and division: $$3x=6$$ $$\color{red}{\frac{\color{black}{3x}}3}=\color{red}{\frac{\color{black}6}{3}}$$ $$x=2$$ Now we can turn to exponentiation. Consider the equation $x^y=4$, and let's say we want to solve for $y$. Logarithms are the right way to handle that, so we end up with the following: $$\color{red}{\log_x\color{black}{(x^y)}}=\color{red}{\log_x\color{black}4}$$ $$y=\log_x4$$