Find the value of `log_(2sqrt3) 1728`.

Explanation

To find the value of \( \log_{2\sqrt{3}} 1728 \), we can follow these steps:

### Step 1: Express 1728 in terms of its prime factors
First, we need to factor 1728. We can start by checking if it's a perfect cube or square.

1728 can be expressed as:
\[
1728 = 12^3
...