# Exponential & logarithmic functions

This course is a part of
**Algebra (all content)**, a 20-course Topic series from Khan Academy.

This topic covers: - Radicals & rational exponents - Graphs & end behavior of exponential functions - Manipulating exponential expressions using exponent properties - Exponential growth & decay - Modeling with exponential functions - Solving exponential equations - Logarithm properties - Solving logarithmic equations - Graphing logarithmic functions - Logarithmic scale

This course contains 31 segments:

**Exponent properties review**

Practice using the exponent properties to rewrite powers, where the exponent is an integer that can either be positive or negative.

**Radicals**

Radicals (also known as roots) are a generalization of square roots. They are the inverse operation of any power. For example, the 5th root of 32 is 2, because 2⁵=32.

**Rational exponents intro**

Learn the definition for raising a number by a fractional exponent, like 8^⅔.

**Properties of exponents (rational exponents)**

In this tutorial you will rewrite variable expressions with rational exponents using the properties of exponents.

**Advanced exponent & radical evaluation**

Evaluate elaborate expressions that contain radicals and fractional exponents.

**Simplifying square roots**

We know how to evaluate square roots of perfect squares. For example, √16=4. What about the other square roots? It's harder to give an exact number, but we can simplify them so we have a better understanding of their value. For example, √32=4⋅√2. Learn more about it in this tutorial.

**Simplifying radicals (higher-index roots)**

Just like we can simplify square roots, we can simplify other radicals. This tutorial covers the simplification of higher-index roots. For example, ∜48=2⋅∜3.

**Radicals (miscellaneous videos)**

Various videos we have that cover advanced/special skills related to radical expressions.

**Exponential vs. linear growth**

Learn about exponential growth and decay, and specifically how it always grows (or diminishes) by equal factors.

**Exponential expressions**

Learn how to construct exponential functions to model real-world situations.

**Graphs of exponential growth**

Learn how an exponential function behaves as the value of its input increases to positive infinity or decreases to negative infinity. Learn how to graph basic exponential functions.

**Exponential vs. linear growth over time**

Learn how to distinguish between linear and exponential growth, and learn the differences between the end behavior of polynomial and exponential functions.

**Exponential decay**

Learn how to construct exponential functions and then analyze them to model and solve real-world problems.

**Exponential functions from tables & graphs**

Learn how to analyze the formulas of basic exponential functions in order to find their common ratio, initial value, and other parameters.

**Equivalent forms of exponential expressions**

Learn how to manipulate exponential expressions in different ways. For example, rewrite 8^x as 2^(3x).

**Solving exponential equations using properties of exponents**

Learn how to solve advanced exponential equations by manipulating the expressions in the equations using the properties of exponents. For example, solve 2^(x+1)=8^x by rewriting 8^x as 2^(3x) and then equating x+1=3x.

**Introduction to rate of exponential growth and decay**

Learn about different ways of describing the rate of change of exponential functions.

**Interpreting the rate of change of exponential models (Algebra 2 level)**

Learn how to analyze exponential modeling functions in order to find their rate of change.

**Constructing exponential models according to rate of change (Algebra 2 level)**

Learn how to find the modeling function of an exponential real world context, according to the description of its rate of change.

**Advanced interpretation of exponential models (Algebra 2 level)**

Learn how to interpret an exponential modeling function by first manipulating it according to your needs. For example, rewrite 5^(2x+1) as 5*25^x to find that the unit growth factor is 25.

**Distinguishing between linear and exponential growth (Algebra 2 level)**

Learn how to analyze real-world quantitative relationships given as tables of values to determine whether they represent linear growth or exponential growth.

**Introduction to logarithms (Algebra 2 level)**

Learn how we define logarithms and use this definition in order to evaluate various logarithms. For example, evaluate log_2(8) as 3 by realizing that 2^3=8.

**The constant e and the natural logarithm (Algebra 2 level)**

Learn about a very special constant in math that has a pivotal role in the world of exponential and logarithmic function, the constant e.

**Properties of logarithms (Algebra 2 level)**

Learn about special properties of logarithms that help us rewrite logarithmic expressions in different equivalent (much like we use properties of exponents to rewrite exponential expressions!).

**The change of base formula for logarithms (Algebra 2 level)**

Learn how to rewrite any logarithmic expression in a different base. For example, rewrite log_2(3) as ln(3)/ln(2). This is very helpful for evaluating logarithms with a calculator, which only evaluates base-10 and base-e logarithms.

**Logarithmic equations (Algebra 2 level)**

Learn how to solve equations that contain logarithmic expressions. For example, solve log(x)+log(3)=log(7).

**Solving exponential equations with logarithms (Algebra 2 level)**

Learn how to solve any exponential equation by using logarithms. For example, solve 2^x=3 by calculating log_2(3).

**Solving exponential models (Algebra 2 level)**

Learn how to solve word problems that require exponential equations.

**Graphs of exponential functions (Algebra 2 level)**

Learn about the graphs of advanced exponential functions of the form y=a*b^(x+c)+d.

**Graphs of logarithmic functions (Algebra 2 level)**

Learn about the graphs of logarithmic functions, and how they relate to graphs of exponential functions.

**Logarithmic scale (Algebra 2 level)**

Enrich your knowledge with some videos about logarithmic scales and how useful they are.

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Rating | Not enough ratings |
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Length | 31 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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Rating | Not enough ratings |
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Length | 31 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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