An electronics technician is reading a technical manual that uses the logarithmic expression $\log V^5$ to calculate voltage gain. According to the Power Property of Logarithms, which of the following expressions is equivalent to $\log V^5$?

An acoustics engineer simplifying a noise level formula determines that the logarithmic expression $\log_{10}(I^2)$ is mathematically equivalent to ${}2 \log_{10} I$.

A laboratory technician is simplifying logarithmic data used to measure signal intensity. Using the Power Property of Logarithms, match each logarithmic expression on the left with its equivalent product form on the right.

Simplifying Financial Growth Models

A software developer is analyzing the time complexity of a data processing algorithm. The mathematical model for the process includes the term $\log(N^{100})$. To simplify the expression for a technical report, the developer needs to rewrite it as a product. The simplified term is written as ____ $\log(N)$.

Simplifying Logarithmic Expressions in Quality Control Software

An assistant financial planner is simplifying a compounding interest formula that includes the logarithmic expression $\log_7 5^4$ to project investment returns in a client report. To make the calculations easier to explain to the client, the analyst wants to write this term as a product using the Power Property of Logarithms. Arrange the steps in the correct order to show how the analyst simplifies this expression using the property.