To solve the equation $2^x = 4$:

1. Recognize that $4$ can be expressed as a power of $2$. Specifically: $4 = 2^2$

2. Substitute $4$ with $2^2$ in the equation: $2^x = 2^2$

3. Since the bases are the same, equate the exponents: $x = 2$

Thus, the solution is: $x = 2$

Would you like further details or have any questions about this?

Here are five follow-up questions to deepen your understanding:

1. How do you solve exponential equations where the bases are not the same?
2. What if the equation was $2^x = 5$, how would you solve it?
3. How can logarithms help in solving exponential equations?
4. Can exponential equations have more than one solution?
5. What are real-world applications of solving equations like $2^x = 4$?

Tip: When solving exponential equations, always try to express both sides using the same base if possible—it simplifies the process greatly!