Find the value of k and solve the equation
A function f(x) is defined as f(x) = 2^x + k, where k is a constant. The function passes through the point (4, 40).
Find the value of k.
For this value of k, solve the equation f(x) = 3^x.
The Labyrinth of Linear Equations
In a world where paths are determined by equations, you find yourself at the entrance of a labyrinth. The labyrinth is designed as a giant coordinate plane, with the entrance at the origin (0,0). To navigate through, you must follow a path defined by a series of linear equations, each leading to the next until you find the exit. The path is as follows: Start at the origin. Follow the line defined by the equation y=2x+3 until you intersect with the line defined by x=3. At the intersection, turn and follow the line defined by x=3 upwards until you intersect with the line defined by x+6. Once you reach this second intersection, follow the line x+6 to find the exit. Your task is to calculate the coordinates of the exit of the labyrinth.
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