Final answer:
To solve the equation e^{7x} = 9, we use a graphing calculator's zero function, yielding an approximate solution of x = 0.027.
Step-by-step explanation:
To solve the exponential equation e^{7x} = 9 for x, we cannot simplify the equation into a form that can be easily solved algebraically. Therefore, we use a graphing tool or calculator with the ability to find zeros of functions. Inputting the equation into the calculator, you can utilize the zero function to find where the graph of y = e^{7x} intersects the line y = 9. After computation, the calculator gives an approximate solution: x = 0.027. To verify this, you can substitute x = 0.027 back into the original equation and check that both sides are approximately equal.