We are given the equation:

$\log_2(x - 4) = 6$

To solve for $x$, we will use the definition of the logarithm. The equation $\log_b(a) = c$ is equivalent to $b^c = a$. Here, $b = 2$, $a = x - 4$, and $c = 6$. So we can rewrite the equation as:

$2^6 = x - 4$

Now, simplify $2^6$:

$64 = x - 4$

Next, solve for $x$ by adding 4 to both sides:

$x = 64 + 4$

$x = 68$

Thus, the solution is:

$x = 68$

Would you like a more detailed explanation or have any questions about the process?

Here are 5 related questions:

1. How do logarithms with different bases work?
2. What is the inverse of a logarithmic function?
3. How can logarithmic equations with unknowns in the argument be solved?
4. How do we apply the change of base formula for logarithms?
5. What happens when a logarithmic equation has a negative argument?

Tip: Always check that the argument inside a logarithm is positive, as logarithms are not defined for non-positive numbers.