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How do I square a logarithm? - Mathematics Stack Exchange You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
Inequality proof, why isnt squaring by both sides permissible? So if we want to square both sides of x <2 x <2 and still have a true inequality, then we need the additional restriction that x> 0 x> 0 (Actually x ≥ 0 x ≥ 0 is sufficient ) But why is this restriction enough to make squaring both sides of the inequality ok? That's exactly what the original question wants you to answer
Why can I square both sides? - Mathematics Stack Exchange I am not used to English I ask for your understanding in advance There is the equation: x = 21 2 x = 2 1 2 we can square both side like this: x2 = 2 x 2 = 2 But I don't understand why that it's okay to square both sides What I learned is that adding, subtracting, multiplying, or dividing both sides by the same thing is okay For example: x = 1 x = 1 x − 1 = 1 − 1 x 1 = 1 1 x − 1 = 0 x
algebra precalculus - How to square both the sides of an equation . . . 0 You can square both sides of the equation the way you did But there is a problem in the third line of your working You had x4(x + 3) = (x + 3)3 x 4 (x + 3) = (x + 3) 3 and then divided both sides by (x + 3) (x + 3) to get x4 = (x + 3)2 x 4 = (x + 3) 2 This is a problem because you are losing solutions to the overall equation
Why cant you square both sides of an equation? That's because the 9 9 on the right hand side could have come from squaring a 3 3 or from squaring a −3 3 So, when you square both sides of an equation, you can get extraneous answers because you are losing the negative sign That is, you don't know which one of the two square roots of the right hand side was there before you squared it
The meaning behind $(X^TX)^{-1}$ - Mathematics Stack Exchange What exactly is the meaning of the inverse of (XTX)−1 (X T X) 1? XTX X T X we know as being a square matrix whose diagonal elements are the sums of squares So what are we doing when we take the inverse of this? I have always used this property in my calculations but would like to understand more of the meaning behind it
Why get the sum of squares instead of the sum of absolute values? Why do we square the differences? On one hand, it seems squaring them will allow us to get a positive number when the expected value is less than the actual value But why can't this just be accounted for by taking the sum of the absolute values? Like so: