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$\log_2 (3) \approx 1.58496$ as you can easily verify From what i understand so far, a good regression model minimizes the sum of the squared differences between $ (\log_2 (3))^2 \approx (1.58496)^2 \approx 2.51211$

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$2 \log_2 (3) \approx 2 \cdot 1.58496 \approx 3.16992$ If $\underbrace {20242024\cdots2024}_ {n\text { $2^ {\log_2 (3)} = 3$

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. 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. 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 But how come squaring both. Q&a for people studying math at any level and professionals in related fields

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. Is $2025$ the only square number that is form of $\underbrace {20242024\cdots2024}_ {n\text { times}}2025$ This question was never asked in any competiton