Example 10.29: Evaluating $4^{\log_4 9}$ and $\log_3 3^5$ Using Inverse Properties

A technician is calibrating a digital sensor that uses base 10 for its logarithmic measurements. To verify the sensor's accuracy, the technician checks a test signal that has been processed through both a logarithm and an exponential function, resulting in the expression ${}10^{\log_{10} 15}$. According to the Inverse Properties of Logarithms, what is the simplified value of this expression?

A software developer is auditing a script that handles financial growth models using various logarithmic bases. To ensure the code runs efficiently, the developer must simplify several expressions using the Inverse Properties of Logarithms. Match each mathematical expression on the left with its correctly simplified form on the right.

A software engineer is auditing a legacy script that processes data in base 2. The script contains a line of code that simplifies the expression $\log_2 2^n$ to the value 2. According to the Inverse Properties of Logarithms, is this simplification correct?

Simplifying Financial Growth Models

An inventory manager at a logistics warehouse is reviewing an automated stock report. The system calculates a verification code for a specific shipment using the expression ${}10^{\log_{10} 85}$. According to the Inverse Properties of Logarithms, the manager should simplify this code to the value ____ for the final report.