The problem you uploaded involves evaluating logarithmic expressions. Here's a breakdown of each one:

Problem 1:

Evaluate the expression: $\log_3 36 - 4 \log_{30} 10 + 16 \log_{81} \sqrt{15}$ The steps shown in the solution simplify the expression using properties of logarithms, such as the change of base formula and logarithmic identities: $\log_b a = \frac{\log_c a}{\log_c b}$ and the power rule for logarithms: $n \log_b a = \log_b a^n$ Finally, the simplified value is found to be: $2$

Problem 2:

Evaluate the expression: $\log_2 6 \cdot \log_6 6 - (\log_3 3 + \log_3 2)$ In this case, the properties of logarithms (like $\log_b b = 1$) are used to simplify the expression step by step.

Problem 3:

Evaluate the expression: $\log_2 14 \cdot \log_7 14 - (\log_2 7 + \log_7 2)$ This involves using logarithmic properties like the product rule, where: $\log_b a + \log_b c = \log_b (a \cdot c)$

Would you like me to go over the details of the simplifications for each problem? Or do you have any specific questions about any of the steps?