We are tasked with solving the equation:

$3 \log_x(64) = 6$

Step-by-step solution:

1. Isolate the logarithmic term:

   $\log_x(64) = \frac{6}{3} = 2$

2. Convert the logarithmic equation to exponential form:

   The logarithmic expression $\log_x(64) = 2$ implies:

   $x^2 = 64$

3. Solve for $x$:

   Taking the square root of both sides:

   $x = \pm \sqrt{64} = \pm 8$

However, since $x$ represents the base of a logarithm, it must be positive. Therefore, we discard the negative value.

Thus, the solution is:

$x = 8$

Would you like further details or have any questions?

Here are 5 related questions you could explore:

1. What is the general method to solve logarithmic equations like $\log_b(y) = c$?
2. How does the change of base formula for logarithms work?
3. What if the logarithmic base $x$ is not restricted to positive values?
4. Can logarithms with negative bases ever be valid?
5. What is the derivative of a logarithmic function in terms of its base?

Tip: Always remember that the base of a logarithm must be positive and cannot be 1.