Solving Exponential Equations

To solve the exponential equation by graphing, we first have to create two functions. Each side of the given equation will become a function. $$\begin{array}{r}1-5^{5-x}=\text{-}9\Rightarrow \begin{array}{l}y=1-5^{5-x}\\ y=\text{-}9\end{array}\end{array}$$ The solution to the equation is the $x\text{-}$value where the two graphs intersect.

From the diagram, we see that the graphs intersect at $x\approx 3.5.$ This is our best guess approximation. If we limit the diagram's $x$-axis around the point of intersection, we can get a better approximation.