To solve the equation $\log_4(4x + 7) = 2$, let's break it down step by step:

1. Rewrite the logarithmic equation in exponential form: $4x + 7 = 4^2$

2. Simplify $4^2$: $4x + 7 = 16$

3. Solve for $x$: $4x = 16 - 7$ $4x = 9$ $x = \frac{9}{4}$

Final Answer:

$x = \frac{9}{4}$

Would you like me to explain any of the steps in more detail or assist with another problem?

Here are 5 related questions you might explore:

1. What are the general rules for converting logarithmic equations to exponential form?
2. How can you verify the solution of a logarithmic equation?
3. What happens when there is no solution for a logarithmic equation? How can we identify such cases?
4. How do we solve equations involving logarithms with different bases?
5. Can logarithmic equations have more than one solution? Under what circumstances?

Tip: Always check the domain of the logarithmic function to ensure the solution is valid (i.e., the argument inside the logarithm must be positive).