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Expanding Logarithmic Expressions (page 2 of 5) Sections: Basic log rules, Expanding, Simplifying, Trick questions, ChangeofBase formula
The 5 is divided into the 8x^{4}, so split the numerator and denominator by using subtraction: Don't take the exponent out front yet; it is only on the x, not the 8, and you can only take the exponent out front if it is "on" everything inside the log. The 8 is multiplied onto the x^{4}, so split the factors by using addition: log_{2}(8x^{4}) – log_{2}(5) = log_{2}(8) + log_{2}(x^{4}) – log_{2}(5) The x has an exponent (which is now "on" everything inside its log), so move the exponent out front as a multiplier: log_{2}(8) + log_{2}(x^{4}) – log_{2}(5) = log_{2}(8) + 4log_{2}(x) – log_{2}(5) Since 8 is a power of 2, I can simplify the first log to an exact value:
log_{2}(8) + 4log_{2}(x) – log_{2}(5) = 3 + 4log_{2}(x) – log_{2}(5) Each log contains only one thing, so this is fully simplified. The answer is: 3 + 4log_{2}(x) – log_{2}(5) Use the log rules, and
don't try to do too much in one step: Then the final answer is: Copyright © Elizabeth Stapel 20022011 All Rights Reserved log_{3}(4) + 2log_{3}(x – 5) – 4log_{3}(x) – 3log_{3}(x – 1) You can use the Mathway widget below to practice "Logarithmic Expressions and Equations", subtopic "Expanding Logarithmic Expressions". Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.) (Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free sevenday trial of the software.) << Previous Top  1  2  3  4  5  Return to Index Next >>



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