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 logarithms
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awarded  logarithms
2d
comment Alternative notation for exponents, logs and roots?
If it's the Triangle of Power, we need a Triangle of Courage and Triangle of Wisdom to go along with it, to complete the Triforce.
2d
awarded  Good Answer
Apr
30
revised How do you solve $x^2 = \left(\frac 12\right)^x $?
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Apr
30
answered How do you solve $x^2 = \left(\frac 12\right)^x $?
Apr
28
answered Evaluation of $\lim_{x\rightarrow 0}\left(\frac{16^x+9^x}{2}\right)^{\frac{1}{x}}$
Apr
19
revised Solving $\cos(t)y' + y\sin(t) = \cos^4(t)$?
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Apr
19
revised Solving $\cos(t)y' + y\sin(t) = \cos^4(t)$?
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Apr
18
comment How to test convergence for $\sum^{\infty}_{n} \frac{1}{(\ln{n})^3}$?
Looks good, although one might challenge you to prove that $\ln n<n^{1/3}$. But if you can prove that, it's solid.
Apr
17
comment Product of all real numbers in a given interval $[n,m]$
It looks like variants on this have been around for a while: https://en.wikipedia.org/wiki/Product_integral.
Apr
17
answered Product of all real numbers in a given interval $[n,m]$
Apr
16
comment How many numbers $ N \le 10^{10}$ are the product of $3$ distinct primes?
You've indicated a nested for loop counting incidents is not what you want. But a nested for loop is essentially a nested summation where you are summing 1 or 0 along the way.
Apr
16
comment Show by series definition of exponential function that $\exp(-x) \rightarrow 0 $ for $x \rightarrow \infty.$
@paulgarrett You can establish $e^xe^{-x}=1$ using only the power series. Establish absolute convergence so summation order can be played with, and the following does this, where $k$ reindexes as $k=m+n$: $$\sum_{n=0}^\infty\frac{x^n}{n!}\cdot\sum_{m=0}^\infty\frac{(-x)^m}{m!}=\sum_{m‌​=0}^\infty\sum_{n=0}^\infty\frac{(-1)^mx^{m+n}}{m!n!}$$ $$=\sum_{k=0}^\infty\sum_{m=0}^k\frac{(-1)^mx^{k}}{m!(k-m)!}$$ $$=\sum_{k=0}^\infty\frac{x^k}{k!}\sum_{m=0}^k\frac{(-1)^mk!}{m!(k-m)!}$$ $$=\sum_{k=0}^\infty\frac{x^k}{k!}\sum_{m=0}^k(-1)^m\binom{k}{m}$$ $$=\sum_{k=0}^\infty\frac{x^k}{k!}\cdot\delta_{k=0}=1$$
Apr
16
comment How many numbers $ N \le 10^{10}$ are the product of $3$ distinct primes?
"exact answers" in terms of the $\pi$ function? And I presume "closed form" expressions, not anything with a summation?
Apr
16
answered If $A$ is a rotation matrix by $\theta$, then what does $A^T$ do?
Apr
15
revised There is no function from $\mathbb{R} \to (0, \infty)$ satisfying $f'(x)=f(f(x))$
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Apr
15
revised There is no function from $\mathbb{R} \to (0, \infty)$ satisfying $f'(x)=f(f(x))$
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Apr
15
revised There is no function from $\mathbb{R} \to (0, \infty)$ satisfying $f'(x)=f(f(x))$
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Apr
15
answered There is no function from $\mathbb{R} \to (0, \infty)$ satisfying $f'(x)=f(f(x))$
Apr
11
answered Simplifying trigonomic equation of $\sin 2x - \sin x = 0$