1. The problem is to solve an exponential equation, for example, solve for $x$ in the equation $$2^x = 16$$. 2. The formula used here is based on the property of exponents: if $a^x = a^y$, then $x = y$, provided $a > 0$ and $a \neq 1$. 3. First, express 16 as a power of 2: $$16 = 2^4$$. 4. Now the equation becomes $$2^x = 2^4$$. 5. Since the bases are the same and the equation holds, set the exponents equal: $$x = 4$$. 6. Therefore, the solution to the equation $$2^x = 16$$ is $$x = 4$$. This method works for any exponential equation where you can express both sides with the same base.