Exponential Functions and Logarithms

This lecture covers the definitions and graphs of exponential and logarithmic functions, including the properties of the exponential function, such as being strictly increasing and unbounded. It also explores fundamental exponential relations, the exponential function with base e, and the logarithmic function with different bases. The lecture delves into the graphs of exponential functions with various bases, highlighting their continuity, differentiability, and monotonicity. Additionally, it discusses the logarithmic function with different bases, emphasizing their bijectivity and the concept of inverse functions. The most commonly used logarithms, including natural logarithm, base 10 logarithm, and base 2 logarithm, are also presented.