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?

Discover how to solve the logarithmic equation Log2x(x-1) + logx = log12 step-by-step. This problem explores important logarithmic concepts such as properties of logarithms, logarithmic equations, and their simplifications. Suitable for students in Grades 10-12.

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