In professional data analysis, interpreting logarithmic scales is essential for understanding growth patterns and scaling datasets. Match each logarithmic expression below to its simplified numerical value.

As a data technician reviewing a new algorithm's scaling factors, you encounter the mathematical expressions $\log_{13} 1$ and $\log_9 9$. Based on your knowledge of the fundamental properties of logarithms, what are the correct numerical values for these expressions, respectively?

Logarithmic Baseline Configuration

An industrial technician is configuring a control system that uses logarithmic scaling. The technician encounters two baseline parameters defined as $K_1 = \log_{13} 1$ and $K_2 = \log_9 9$. The technician records these parameters in the system log as $K_1 = 1$ and $K_2 = 9$.

Industrial Control System Calibration