Question

Can someone please help me I have no idea how to do this :(?!

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 2 ^x + 3 intersect are the solutions of the equation 4 ^−x = 2 ^x + 3.

Part B: Make tables to find the solution to 4 ^−x = 2 ^x + 3. Take the integer values of x between −3 and 3.

Part C: How can you solve the equation 4^−x = 2^x + 3 graphically?

Answer 1

Part C:  Treat these two expressions as separate functions.  Then f(x) = 4^(-x) and g(x) = 2^x + 3.  Graph these functions separately on the same set of coordinate axes.  Determine the coordinates of the point of intersection of the two graphs.  That's your "solution," or at least the x-component of it.  To find the y-component, substitute your "solution" into either f(x) or g(x).  Write your final solution in the form (x,y).