In this section, we will explore rules of exponents. We will also look at how to evaluate exponential expressions. Exponents are a short hand way of multiplying an expression by itself. Negative exponents are the same as taking the reciprocal. Fraction exponents are another way to write roots of values.
Evaluate Exponential Expressions
Determine if Exponential, Linear, or Neither
Logarithms
In this section, we will explore rules of logarithms. Knowing how to evaluate logarithms both by hand and in a calculator is important. It's also important to be able to find the domain and range of logarithmic functions. Videos will also explore how to find the inverse of logarithmic functions.
Find Exact Value of a Logarithm without a Calculator
Use a Calculator to find Value of a Logarithm
Find the Domain of a Logarithmic Function
Inverse of a Log Function with finding Domain and Range of Both
Graphs of Exponential and Logarithmic Functions
Learn to graph both exponential and logarithmic functions. The graphs are reciprocal functions. If graphing exponential functions, the parent function always goes through the points (-1, 1/b), (0, 1), and (1, b) where b represents the exponential rate of growth/decay. Exponential functions have a horizontal asymptote. Transformations can then be used to graph the given function. To graph logarithmic functions, since it a reciprocal function of exponential function, the x and y coordinates switch, so logarithmic function pass through the points (1/b, -1), (1, 0), and (b, 1). Logarithms have vertical asymptotes. Transformations can be used to graph the given logarithmic function.
Exponential Growth with
Transformations
Graph Logarithm with
Transformations
Rewrite Logarithms and Exponents
Learn to rewrite exponential functions as logarithmic functions, and vice versa. This is a very important part of being able to work with exponents and logarithms.
There are many applications of logarithmic and exponential functions. The most well known is compound interest. Other applications include population growth, half-life, and Newton's Law of Cooling. Various examples will be covered.