When I take the Log of both sides of an equation, should I only do it once?

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Based on what I have learned, I am wondering how I should proceed with taking the Log of both sides of an equation when there is more than one term present on any given side. For example, is the following a valid move or do I need to combine the terms like in the second example?

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1 Answer

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The logarithm function is non-linear. So when you "take the log" of both sides of an equation, you must contain the entire side of the equation inside the logarithm argument. So in this case, the correct method is the second one you have: $$x^3+3=5x\\\log(x^3+3)=\log(5x)$$

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