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Simplifying Logarithmic Expressions (page 3 of 5) Sections: Basic log rules, Expanding, Simplifying, Trick questions, ChangeofBase formula The logs rules work "backwards", so you can simplify ("compress"?) log expressions. When they tell you to "simplify" a log expression, this usually means they will have given you lots of log terms, each containing a simple argument, and they want you to combine everything into one log with a complicated argument. "Simplifying" in this context usually means the opposite of "expanding".
Since these logs have the same base, the addition outside can be turned into multiplication inside: log_{2}(x) + log_{2}(y) = log_{2}(xy) The answer is log_{2}(xy). Copyright © Elizabeth Stapel 20022011 All Rights Reserved
Since these logs have the same base, the subtraction outside can be turned into division inside: log_{3}(4) – log_{3}(5) = log_{3}(^{4}/_{5}) The answer is log_{3}(^{4}/_{5}).
The multiplier out front can be taken inside as an exponent: 2log_{3}(x) = log_{3}(x^{2})
I will get rid of the multipliers by moving them inside as powers: 3log_{2}(x)
– 4log_{2}(x
+ 3) + log_{2}(y)
Then I'll put the added terms together, and convert the addition to multiplication: log_{2}(x^{3})
– log_{2}((x + 3)^{4})
+ log_{2}(y)
Then I'll account for the subtracted term by combining it inside with division: You can use the Mathway widget below to practice simplifying a logarithmic expression. Try the entered exercise, or type in your own exercise. Then click the "paperairplane" button to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)
(Clicking on "Tap to view steps" on the widget's answer screen will take you to the Mathway site for a paid upgrade.) << Previous Top  1  2  3  4  5  Return to Index Next >>



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