2) \( \ln \left(u \cdot v \cdot w^{5}\right) \)

Did you know that logarithmic properties can help simplify complex expressions? In this case, you can break down the natural logarithm of a product! The logarithm of a product can be split into the sum of the logarithms: \( \ln(u \cdot v \cdot w^5) = \ln(u) + \ln(v) + \ln(w^5) \). Plus, since \( \ln(w^5) \) can be further simplified to \( 5 \cdot \ln(w) \), the entire expression becomes \( \ln(u) + \ln(v) + 5 \cdot \ln(w) \). Understanding this concept isn’t just theoretical; it has practical applications in fields like economics and science. For example, when dealing with multiple variables in growth rates, you often need to combine various multiplicative factors together. By utilizing logarithms, you can simplify the equations you use to model those relationships, making it easier to analyze changes, solve for unknowns, and interpret data efficiently. Applying this knowledge can lead to clearer insights in your calculations!