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How do I square a logarithm? - Mathematics Stack Exchange $\log_2 (3) \approx 1 58496$ as you can easily verify $ (\log_2 (3))^2 \approx (1 58496)^2 \approx 2 51211$ $2 \log_2 (3) \approx 2 \cdot 1 58496 \approx 3 16992$ $2^ {\log_2 (3)} = 3$ Do any of those appear to be equal? (Whenever you are wondering whether some general algebraic relationship holds, it's a good idea to first try some simple numerical examples to see if it is even possible
Why cant you square both sides of an equation? That's because the $9$ on the right hand side could have come from squaring a $3$ or from squaring a $-3$ 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
Why can I square both sides? - Mathematics Stack Exchange we can square both side like this: $ 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 = 1-1 $ $ x-1 = 0 $ $ x \times 2 = 1 \times 2 $ $ 2x = 2 $ like this But how come squaring both
algebra precalculus - How to square both the sides of an equation . . . I understand that you can't really square on both the sides like I did in the first step, however, if this is not the way to do it, then how can you really solve an equation like this one (in which there's a square root on the LHS) without substitution?
Inequality proof, why isnt squaring by both sides permissible? 7 Short answer: We can't simply square both sides because that's exactly what we're trying to prove: $$0 < a < b \implies a^2 < b^2$$ More somewhat related details: I think it may be a common misconception that simply squaring both sides of an inequality is ok because we can do it indiscriminately with equalities
Isnt square root a bit like Log()? - Mathematics Stack Exchange I took a look at square root Squaring the number means x^2 And if I understood the square root correctly it does a bit inverse of squaring a number and gets back the x I had a friend tell me a while ago that Log() is also opposite of exponent, wouldn't that mean that square root is like a variant of Log () that only inverse a squared number?
Why sqrt(4) isnt equall to-2? - Mathematics Stack Exchange If you want the negative square root, that would be $-\sqrt {4} = -2$ Both $-2$ and $2$ are square roots of $4$, but the notation $\sqrt {4}$ corresponds to only the positive square root
factorial - Why does 0! = 1? - Mathematics Stack Exchange The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes