Consider the function $$f_a : \mathbb{R} \to \mathbb{R}$$ defined by $f_a(b)= a^b$. What verb should I use to describe the action of this function on $b$?
For example, if I defined the function $$g_a : \mathbb{R} \to \mathbb{R}$$ by $g_a(b) = b + a$, I would say that $g_a$ adds $a$ to $b$.
In words, what does $f_a$ do to $b$? $\quad$
Edit
I think it would help clarify my question to explain the context of the problem. I'm teaching someone how to solve equations involving logarithms. For example, you might have an equation like $$\log_2 10 = 5$$ I've told him that he should solve this equation by exponentiating both sides with base 2, i.e. $$2^{\log_2 10} = 2^5$$ which yields $$10 = 2^5$$ I'm trying to find a more economical way of saying "exponentiate both sides with base 2."
When you're dealing with the natural logarithm, this is easy. You "apply the exponential function to both sides." I'm trying to find an analogous phrase for when the base is something other than $e$.