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. 1. **Factor 36**: \[ 36 = 6^2 \] 2. **Apply the logarithm power rule**: The power rule states that \( \log(a^b) = b \log(a) \). Therefore: \[ \log 36 = \log(6^2) = 2 \log 6 \] Now, let's compare this result with the given options: - \( \log 4 \cdot \log 9 \) does not simplify to \( \log 36 \). - \( 2 \log 6 \) is the correct expansion. - \( 36 \log 1 \) equals 0, since \( \log 1 = 0 \). - \( 6 \log 6 \) does not simplify to \( \log 36 \). Thus, the correct expression that expands \( \log 36 \) to its simplest form is: \[ \boxed{2 \log 6} \]