Critical thinking questions: \( \begin{array}{ll}\text { 25) } 2(\log 2 x-\log y)-(\log 3+2 \log 5) & \text { 26) } \log x \cdot \log 2\end{array} \)

To tackle the first question, let’s simplify the expression: \( 2(\log 2 x - \log y) - (\log 3 + 2 \log 5) \). Using properties of logarithms, rewrite it as \( 2(\log 2 + \log x - \log y) \), which becomes \( 2 (\log (2x/y)) - (\log 3 + \log (5^2)) \). Combining these, we can write it as \( \log ( (2x/y)^2 / 75) \). For the second question, \( \log x \cdot \log 2 \) introduces logarithmic multiplication, leading to an expression that captures how the values of \( x \) and the base \( 2 \) relationship intertwine. This could hint at the growth rates between the two values or their interplay in logarithmic forms, especially in various logarithm base contexts.