Question

How do $\arctan(f(x))$ and $\ln(g(x))$ relate?

score 156 · Answer 1 · 2026-04-15 14:03:28

156

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How do $\arctan(f(x))$ and $\ln(g(x))$ relate?

Published on 15 Apr 2026 - 14:03

score 75 · Answer 2 · 2026-04-17 06:20:14

75

Views

Proving that $(2^3)^{\log_2 n}=n^3$

Published on 17 Apr 2026 - 6:20

score 204 · Answer 3 · 2026-04-15 20:51:42

204

Views

How can we prove this logarithm property : $\log_{a^m} (b^n) = \frac{n}{m}\log_a b$

Published on 15 Apr 2026 - 20:51

score 91 · Answer 4 · 2026-04-15 18:08:07

91

Views

Prove that $\sum_{r=2}^{n} \left \lfloor n^{\frac{1}{r}} \right \rfloor = \sum_{r=2}^{n} \left \lfloor \log_{r}(n) \right \rfloor$.

Published on 15 Apr 2026 - 18:08

score 308 · Answer 5 · 2026-04-11 12:31:56

308

Views

What is the Möbius transformation that maps $\mathbb{C}\setminus]-\infty;0]$ onto the unit disk?

Published on 11 Apr 2026 - 12:31

score 51 · Answer 6 · 2026-04-12 05:30:17

51

Views

Confusion in solutions of logarithm.

Published on 12 Apr 2026 - 5:30

score 81 · Answer 7 · 2026-04-11 16:08:28

81

Views

Integration with trigonometric functions question

Published on 11 Apr 2026 - 16:08

score 66 · Answer 8 · 2026-04-13 23:25:05

66

Views

Finding the limit of $\frac{N_n}{\ln(n)}$ where $N_n$ is the number of digits of $n$

Published on 13 Apr 2026 - 23:25

score 54 · Answer 9 · 2026-04-11 13:28:59

54

Views

Is there a method to change an integrand as a result of adding a constant within the original integral result?

Published on 11 Apr 2026 - 13:28

score 79 · Answer 10 · 2026-04-16 04:35:38

79

Views

Find the asymptote and the upper bound for $1\big/ \ln\left(\frac{x+1}{x-1}\right)$ as $x\to\infty$.

Published on 16 Apr 2026 - 4:35

score 94 · Answer 11 · 2026-04-16 12:44:35

94

Views

How do we solve the equation $2^{x^2-3}=x^{-1/3}$ algebraically?

Published on 16 Apr 2026 - 12:44

score 142 · Answer 12 · 2026-03-25 14:23:34

142

Views

Show that $(a^3+a+1)(b^3+b+1)(c^3+c+1)\le 27$

Published on 25 Mar 2026 - 14:23

score 188 · Answer 13 · 2026-04-16 09:17:24

188

Views

Justifying $\sum_{n=0}^\infty\log(1+x^{2^n}) = -\log(1-x)$ for $0\le x<1$

Published on 16 Apr 2026 - 9:17

score 822 · Answer 14 · 2026-04-15 01:06:59

822

Views

How to solve $\log_2(x)+\log_{10}(x-7)=3$ using high-school math?

Published on 15 Apr 2026 - 1:06

score 308 · Answer 15 · 2026-04-17 06:47:22

308

Views

How to solve the equation $\log_{2x+3}(6x^2+23x+21)=4-\log_{3x+7}(4x^2+12x+9)$?

Published on 17 Apr 2026 - 6:47

List Question

How do $\arctan(f(x))$ and $\ln(g(x))$ relate?

Proving that $(2^3)^{\log_2 n}=n^3$

How can we prove this logarithm property : $\log_{a^m} (b^n) = \frac{n}{m}\log_a b$

Prove that $\sum_{r=2}^{n} \left \lfloor n^{\frac{1}{r}} \right \rfloor = \sum_{r=2}^{n} \left \lfloor \log_{r}(n) \right \rfloor$.

What is the Möbius transformation that maps $\mathbb{C}\setminus]-\infty;0]$ onto the unit disk?

Confusion in solutions of logarithm.

Integration with trigonometric functions question

Finding the limit of $\frac{N_n}{\ln(n)}$ where $N_n$ is the number of digits of $n$

Is there a method to change an integrand as a result of adding a constant within the original integral result?

Find the asymptote and the upper bound for $1\big/ \ln\left(\frac{x+1}{x-1}\right)$ as $x\to\infty$.

How do we solve the equation $2^{x^2-3}=x^{-1/3}$ algebraically?

Show that $(a^3+a+1)(b^3+b+1)(c^3+c+1)\le 27$

Justifying $\sum_{n=0}^\infty\log(1+x^{2^n}) = -\log(1-x)$ for $0\le x<1$

How to solve $\log_2(x)+\log_{10}(x-7)=3$ using high-school math?

How to solve the equation $\log_{2x+3}(6x^2+23x+21)=4-\log_{3x+7}(4x^2+12x+9)$?

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