In technical fields like acoustics or electrical engineering, the Product Property of Logarithms is used to simplify the calculation of total gain or intensity. If a technician needs to find the total gain of a system where two components have individual gains of $G_1$ and $G_2$, they must expand the expression $\log_a(G_1 \cdot G_2)$. Which of the following correctly represents this property for positive values of $G_1$, $G_2$, and base $a$?

A business analyst is preparing a report on campaign performance and needs to simplify several logarithmic growth formulas. Use the Product Property of Logarithms to match each original expression on the left with its correctly expanded form on the right.

Simplifying Acoustic Intensity Formulas

Signal Gain and Logarithmic Properties

In technical fields such as acoustics, the Product Property of Logarithms is used to simplify complex intensity calculations. This property states that for any positive numbers $M$, $N$, and $b$ (where $b \neq 1$), the logarithm of a product is equal to the sum of the individual logarithms of its factors: $\log_b(M \cdot N) = \log_b M + \log_b N$. True or False?