Exponents and Logarithms

Exponents and logarithms are reciprocal functions. They are used often in the real world, especially in areas like finance, science, and populations. Examples of exponential functions are compound interest, exponential growth or decay, and population estimates. Logarithms help to solve exponential equations when the variable is in the exponent.

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

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. 

Exponential to Logarithmic Form
Logarithmic to Exponential Form

Properties of Logarithms and Exponents

Learn the various properties for both logarithmic and exponential functions. 

Expand Logarithms
Condense Logarithms

Equations

Learn how to solve exponential and logarithmic equations. 

Solve Logarithmic Equation Ex 1