Mathematics - Lecture 18 "Exponential and logarithmic functions" presents the following content: Real Exponents, exponential functions, equations involving exponential expressions, logarithmic functions. | Exponential and Logarithmic Functions Institute of Mathematics, University of the Philippines Diliman Lecture 19 (IMath, UPD) Exponential and Logarithmic Functions Lec. 19 1 / 29 Outline 1 Real Exponents 2 Exponential Functions 3 Equations involving Exponential Expressions 4 Logarithmic Functions (IMath, UPD) Exponential and Logarithmic Functions Lec. 19 2 / 29 Real Exponents recall: definition and properties of rational exponents (IMath, UPD) Exponential and Logarithmic Functions Lec. 19 3 / 29 Real Exponents recall: definition and properties of rational exponents In particular, if a > 1 and p, q ∈ (IMath, UPD) Q with p 1 and p, q ∈ (IMath, UPD) Q with p < q, then ap < aq . Exponential and Logarithmic Functions Lec. 19 3 / .