Final answer:
To solve the logarithmic equation, isolate the logarithm, convert it to an exponential form, simplify, and solve for the variable, which results in x = 13.
Step-by-step explanation:
To solve the equation \(log_3(x-4) + 4 = 6\), we first need to isolate the logarithm on one side. This is done by subtracting 4 from both sides of the equation, getting \(log_3(x-4) = 2\).
Next, we apply the property of logarithms that states if \(log_b(a) = c\), then \(b^c = a\). This means we need to express the equation in exponential form: \(3^2 = x - 4\).
Then, simplify the exponential expression: \(9 = x - 4\). Now, we add 4 to both sides to find the value of x: \(x = 13\).
Therefore, the correct answer is D. \(x = 13\).