Which of the following expressions correctly expands \( \log 36 \) to its simplest form? \( \begin{array}{l}\log 4 \cdot \log 9 \\ 2 \log 6 \\ 36 \log 1 \\ 6 \log 6\end{array} \)

To expand \( \log 36 \) to its simplest form, we can use the properties of logarithms. First, we can express 36 as \( 6^2 \), so we have: \[ \log 36 = \log(6^2) = 2 \log 6 \] This shows that the expression \( 2 \log 6 \) is correct. Moreover, if we break down \( \log 36 \) further, it can also be expressed as: \[ \log(4 \cdot 9) = \log 4 + \log 9 = \log(2^2) + \log(3^2) = 2 \log 2 + 2 \log 3 = 2(\log 2 + \log 3) \] But in simpler terms, \( 2 \log 6 \) is the simplest form when considering \( 36 \) expressed as \( 6^2 \). Thus, the correct expansion is \( 2 \log 6 \).