The equation given in the image is:

$2^{4x} = 8$

Step-by-step solution:

1. Express 8 as a power of 2: $8 = 2^3$ So, the equation becomes: $2^{4x} = 2^3$

2. Since the bases are the same (both are base 2), equate the exponents: $4x = 3$

3. Solve for $x$: $x = \frac{3}{4}$

Thus, the solution is: $x = \frac{3}{4}$

Would you like more details or have any further questions? Here are 5 additional questions related to this topic:

1. What are the properties of exponents used in this problem?
2. How do we solve more complex exponential equations where the bases are different?
3. Can logarithms be used to solve this problem in a different way?
4. How would the solution change if the equation were $2^{4x} = 16$?
5. What is the relationship between exponential and logarithmic functions?

Tip: When solving exponential equations, expressing numbers in terms of the same base simplifies the process of solving for the exponent.