![]() There are two main reasons to use logarithmic scales in charts and graphs. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. 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 To find the domain, we set up an inequality and solve for x : x : This function is defined for any values of x x such that the argument, in this case 2 x − 3, 2 x − 3, is greater than zero. That is, the argument of the logarithmic function must be greater than zero.įor example, consider f ( x ) = log 4 ( 2 x − 3 ). When finding the domain of a logarithmic function, therefore, it is important to remember that the domain consists only of positive real numbers. Similarly, applying transformations to the parent function y = log b ( x ) y = log b ( x ) can change the domain. In Graphs of Exponential Functions we saw that certain transformations can change the range of y = b x. Just as with other parent functions, we can apply the four types of transformations-shifts, stretches, compressions, and reflections-to the parent function without loss of shape. Transformations of the parent function y = log b ( x ) y = log b ( x ) behave similarly to those of other functions. ![]()
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