To solve the equation [tex]\(\log_2 x + \log_2 (x-6) = 4\)[/tex], we need to make use of logarithmic properties. One such property states that [tex]\(\log_b a + \log_b b = \log_b (a \cdot b)\)[/tex].
Here are the steps:
1. Combine the logarithms:
By using the property [tex]\(\log_2 a + \log_2 b = \log_2 (a \cdot b)\)[/tex], we can combine [tex]\(\log_2 x + \log_2 (x-6)\)[/tex] into a single logarithm:
[tex]\[
\log_2 [x(x - 6)] = 4.
\][/tex]
This shows the first step in the solution process. Therefore, the correct option is:
[tex]\[
\log_2 [x(x - 6)] = 4.
\][/tex]
So, the correct choice for the first step in the solution to the given equation is:
[tex]\[
\boxed{\log_2 [x(x - 6)] = 4}
\][/tex]
