You are a technician calibrating audio equipment using software that calculates sound levels. The calibration script requires evaluating the expressions $\log_5 1$ and $\log_7 7$ to establish baseline zero and unit settings. Recalling the basic properties of logarithms, what numerical values should these expressions return, respectively?

Logarithmic Logic States in Software Configuration

A data analyst is configuring a financial forecasting tool. The system requires two baseline constants to be entered as simplified integers. Match each logarithmic expression from the configuration file with its correct numerical value.

A maintenance technician is calibrating a digital power meter and records the value of $\log_5 1$ as 0 and the value of $\log_7 7$ as 1. According to the fundamental properties of logarithms, the technician’s recordings are correct.

Logarithmic Property Verification in Calibration