An acoustics engineer is simplifying a sound intensity model represented by the expression $\log_2(5x^4y^2)$. According to the product and power properties of logarithms, which of the following is the correctly expanded form of this expression?

A logistics analyst is expanding the cost-efficiency model $\log_2(5x^4y^2)$ to isolate the impact of different operational factors. Match each term in the fully expanded expression to the specific component of the original model it represents.

Resource Allocation and Logarithmic Properties

A resource manager is evaluating a cost-efficiency model represented by the expression $\log_2(5x^4y^2)$. True or False: According to the Product and Power Properties of logarithms, the correctly expanded form of this expression is $\log_2 5 + 4\log_2 x + 2\log_2 y$.

An operations coordinator at a logistics company is using a database query cost model represented by the logarithmic expression $\log_2(5x^4y^2)$. To optimize search performance, the system expands this expression into a linear form. The fully expanded model is written as $\log_2 5 + 4\log_2 x + C\log_2 y$. What is the numerical value of the missing coefficient $C$?

Documenting Logarithmic Metric Calculations in Logistics