We are tasked with solving the equation:

$\log_2 x (x - 1) + \log x = \log 12$

First, let's break down the equation and apply logarithmic properties. Here's how we approach it:

Step 1: Simplify the first logarithmic term

The equation is:

$\log_2 x (x - 1) + \log x = \log 12$

But there's an ambiguity in the term $\log_2 x (x - 1)$. It could either be:

1. $\log_2 (x(x - 1))$
2. Or $\log_2 x \cdot (x - 1)$

To proceed correctly, can you confirm which interpretation you'd like?