Final answer:
To graph the equation 2^{2x}=5.3, plot the exponential function f(x) = 2^{2x} and the constant function g(x) = 5.3, then find their point of intersection. This intersection will give the value of x that satisfies the original equation.
Step-by-step explanation:
To solve the equation 2^{2x}=5.3 by graphing, you would need to plot two separate functions on a graph and look for their point of intersection. The first function is f(x) = 2^{2x}, which represents an exponential growth, and the second function is g(x) = 5.3, which represents a horizontal line since it's a constant value.
The intersection of these two graphs will give us the value for x that satisfies the equation. Unfortunately, without access to graphing tools here, I cannot directly demonstrate the graphing process, but you can use a graphing calculator or software to visually find the solution to the equation. Alternatively, to solve it algebraically, you can take the logarithm of both sides of the equation and use the properties of exponents and logarithms to isolate x. However, the original question asked for a solution by graphing.