Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis Use the information below to generate a citation. 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: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the Expanding Logarithms Taken together, the product rule, quotient rule, and power rule are often called properties of logs. Condense a logarithmic expression into one logarithm. Log 2 x 3 3 y 2 z 4 = 1 4 ( 3 log 2 x − log 2 3 − 2 log 2 y − log 2 z ) log 2 x 3 3 y 2 z 4 = 1 4 ( 3 log 2 x − log 2 3 − 2 log 2 y − log 2 z ) Expanding and Condensing Logarithms Learning Outcomes Expand a logarithm using a combination of logarithm rules. Use the Power Property, log a M p = p log a M log a M p = p log a M, inside the parentheses.ġ 4 ( 3 log 2 x − ( log 2 3 + 2 log 2 y + log 2 z ) ) 1 4 ( 3 log 2 x − ( log 2 3 + 2 log 2 y + log 2 z ) )ġ 4 ( 3 log 2 x − log 2 3 − 2 log 2 y − log 2 z ) 1 4 ( 3 log 2 x − log 2 3 − 2 log 2 y − log 2 z )
N = log a M + log a N, in the second term.ġ 4 ( log 2 ( x 3 ) − ( log 2 3 + log 2 y 2 + log 2 z ) ) 1 4 ( log 2 ( x 3 ) − ( log 2 3 + log 2 y 2 + log 2 z ) ).
Use the Power Property, log a M p = p log a M log a M p = p log a M.ġ 4 log 2 ( x 3 3 y 2 z ) 1 4 log 2 ( x 3 3 y 2 z )ġ 4 ( log 2 ( x 3 ) − log 2 ( 3 y 2 z ) ) 1 4 ( log 2 ( x 3 ) − log 2 ( 3 y 2 z ) ) Learn about the properties of logarithms and how to use them to rewrite logarithmic expressions. Log 2 ( x 3 3 y 2 z ) 1 4 log 2 ( x 3 3 y 2 z ) 1 4 Rewrite the radical with a rational exponent.