Introduction: Logarithmic Properties
When you learned how to solve linear equations, you were likely introduced to the properties of real numbers. These properties help us know what the rules are for isolating and combining numbers and variables. For example, it is advantageous to know that multiplication and division "undo" each other when you want to solve an equation for a variable that is multiplied by a number. You may have also been introduced to properties and rules for writing and using exponents. In this section, we will show you properties of logarithms and how they can help you better understand what a logarithm means and eventually how to solve equations that contain them.By the end of this lesson, you will be able to:
- Define properties of logarithms, and use them to solve equations
- Define the product rule for logarithms, and use it to solve equation
- Define the quotient and power rules for logarithms
- Use the quotient and power rules for logarithms to simplify logarithmic expressions
- Combine product, power and quotient rules to simplify logarithmic expressions
- Expand logarithmic expressions that have negative or fractional exponents
- Condense logarithmic expressions
- Use properties of logarithms to define the change of base formula
- Change the base of logarithmic expressions into base 10, or base e
The learning activities for this lesson include:
- Read: Product Rule for Logarithms
- Self-Check: Product Rule for Logarithms
- Read: Quotient and Power Rules for Logarithms
- Self-Check: Quotient and Power Rules for Logarithms
- Read: Expand and Condense Logarithms
- Self-Check: Expand and Condense Logarithms
- Read: Change of Base
- Self-Check: Change of Base
Licenses & Attributions
CC licensed content, Shared previously
- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..
