We are asked to solve the equation $\log_4(3x+1) = 3$ for $x$.

1. Problem Description

We are asked to solve the equation $\log_4(3x+1) = 3$ for $x$.

2. Solution Steps

The equation is given by:

$\log_4(3x+1) = 3$

We can rewrite this logarithmic equation in exponential form. The general rule is:

$\log_b(a) = c$ is equivalent to $b^c = a$.

Applying this to our equation, we get:

$4^3 = 3x+1$

Now we can simplify and solve for $x$:

$64 = 3x+1$

Subtract 1 from both sides:

$63 = 3x$

Divide both sides by 3:

$x = \frac{63}{3}$

$x = 21$

3. Final Answer

$x = 21$