To solve the equation $\log_2(3x + 4) = 3$, follow these steps:

1. Convert the logarithmic equation to an exponential equation: $3x + 4 = 2^3$

2. Calculate $2^3$: $3x + 4 = 8$

3. Solve for $x$: $3x = 8 - 4$ $3x = 4$ $x = \frac{4}{3}$

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