We are given the equation:

$2^x = 4^x$

Step 1: Express 4 as a power of 2

We know that $4 = 2^2$, so we can rewrite $4^x$ as:

$4^x = (2^2)^x = 2^{2x}$

Thus, the equation becomes:

$2^x = 2^{2x}$

Step 2: Equating the exponents

Since the bases are the same (both are powers of 2), we can equate the exponents:

$x = 2x$

Step 3: Solve for $x$

Now, solve the equation:

$x - 2x = 0$ $-x = 0$ $x = 0$

Final Answer:

The solution to the equation $2^x = 4^x$ is $x = 0$.

Would you like further clarification on this solution or more details on exponent rules?

Here are 5 related questions you might find useful:

1. What are the properties of exponents that allow us to equate the exponents?
2. How can you solve equations involving exponents with different bases?
3. What happens when $x$ is negative in an exponential equation?
4. Can there be other solutions for non-integer values of $x$?
5. How would you solve equations where the exponents involve logarithms?

Tip: Always simplify exponential terms into the same base if possible, to make solving easier.