![]() We will learn later how to change the base of any logarithm before condensing. It is important to remember that the logarithms must have the same base to be combined. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Condensing Logarithms We can use the rules of logarithms we just learned to condense sums, differences, and products with the same base as a single logarithm. ![]() Write the expression as a single logarithm whose coefficient is 1. Use the information below to generate a citation. Use properties of logarithms to condense the logarithmic expression below. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: We can use the rules of logarithms we just learned to condense sums, differences, and products with the same base as a single logarithm. Simplify/Condense Simplify/Condense Simplify/Condense Simplify/Condense. Choose 'Simplify/Condense' from the topic selector and click to see the result in our Algebra Calculator Examples. If you are redistributing all or part of this book in a print format, The logarithm calculator simplifies the given logarithmic expression by using the laws of logarithms. Often, using the rules in the order quotient. In the next examples, we will solve some problems involving pH.Want to cite, share, or modify this book? This book uses the To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. ![]() Show Video Lesson Properties of Logs - Simplify Expression Apply the properties of logarithms to write a single expression. ![]() When condensing logarithms we use the rules of logarithms, including the product rule, the quotient rule and the power rule. We can use the rules of logarithms we just learned to condense sums, differences, and products with the same base as a single logarithm. Taken together, the product rule, quotient rule, and power rule are often called “properties of logs.” Sometimes we apply more than one rule in order to expand an expression. Condensing logarithms can be a useful tool for the simplification of logarithmic terms.
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