Making exponent of $a^x$ object of the function Is it possible to make a variable the subject of a formula when it is an exponent in the equation? For example:
$$y=a^x\quad a\;\text{is constant}$$
For example, let the constant $a = 5.$
$$
\begin{array}{c|l}
\text{x} & \text{y} \\
\hline
1 & 5 \\
2 & 25 \\
3 & 125 \\
4 & 652 \\
5 & 3125 \\
\end{array}
$$
I cannot find the relation between x and y. The constant is making the equation a bit complicated. Appreciate if someone can help me here.

Try taking the natural log "ln" of each side of your equation: 
$$y = a^x \implies \ln y = \ln\left(a^x\right) = x \ln a \iff x = \dfrac{\ln y}{\ln a}$$
If $a = 5$, then we have $$x = \dfrac{\ln y}{\ln 5}$$
This gives us an equation with $x$ expressed in terms of $y$. $\;\ln a = \ln 5$ is simply a constant so $\dfrac 1{\ln 5}$ would be the coefficient of $\ln y$.
