For us old-timers, who grew up with slide rules and logarithm tables, $\log$ was $\log_{10}$ by default. $\ln$ was used only in the weird formulas used by mathematicians, to be translated into $\log_{10}$ as soon as possible [Chemical engineer by training, in the '70s]. $\endgroup$

2023年12月2日 · I probably need to use inclusion-exclusion lemma. The total number of subsets of a $10$ element set is $2^{10} = 1024$. Now I calculate the number of subsets for which the statement holds individually for $2, 3, 5$ (in that order): for $2$ it's $169$, for $3$ it's $200$ and for $5$ it's $243$.

2016年6月24日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2014年10月3日 · You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa. What's the in...

A telephone number consists of $10$ digits, all from $0$ to $9$. The first digit is $0$. The remaining digits can be any number ranging from $0$ to $9$. How many possible telephone numbers are ther...

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2016年1月14日 · So my answer would be $4.0 \times 10^{-8}$, which compares well to the more precise answer of $3.98107 \times 10^{-8}$ from a calculator. Had I computed one more term in the series expansion, I would have gotten $3.978 \times 10^{-8}$, which is quite good.

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is vent into a circle. How should the wire be cut so that the total area enclosed is a maximum and B) a minimum.

2023年7月4日 · How to convert the base $10$ logarithm to base $2$? The question didn't provide the value of the logarithm. The question is: "Given a logarithm in base 10, how can you use the change of base

2014年3月31日 · In doing so, there's a theorem that shows this subset is a subspace and would be itself a vector space (meaning all 10 axioms hold). Hence, it would obey all 10 axioms of a vector space, but you only have to show a proof that it is closed under linear combination (scalar multiplication & vector addition) to hold all 10 axioms.