How Can Solving $\left( 2n \right)^{\left( \log_b 2 \right)} = \left( 5n \right)^{\left( \log_b 5 \right)}$ be Generalized for any Base of $\log_b n$?

score 44 · Answer 6 · 2026-04-16 23:07:02

44

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$\log_a 10 + \log_b 10 +\ log_c 10 \ge \sqrt{3 \log_a 10 * \log_b 10 * \log_c 10}$

Published on 16 Apr 2026 - 23:07

score 123 · Answer 7 · 2026-04-16 19:14:22

123

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Solve $x^2-2x+1=\log_2( \frac{x+1}{x^2+1})$

Published on 16 Apr 2026 - 19:14

score 119 · Answer 8 · 2026-04-10 20:09:10

119

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does Integrating both sides of an equation in dx will Invalidates the equality?

Published on 10 Apr 2026 - 20:09

score 59 · Answer 9 · 2026-04-17 02:31:57

59

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Logarithmic equation: $\log_2 (\frac{x+1}{x^2+2} )= x^2-2x-1$

Published on 17 Apr 2026 - 2:31

score 45 · Answer 10 · 2026-04-17 07:54:12

45

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Show that if $x>1$, $\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-\dfrac{1}{4x^4}-\dfrac{1}{6x^6}-\cdots$

Published on 17 Apr 2026 - 7:54

score 66 · Answer 11 · 2026-04-17 14:36:41

66

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Prove that if $\alpha \geq1$ and $n\geq 2\alpha \log(2\alpha)$ then $n \geq \alpha \log(2n)$

Published on 17 Apr 2026 - 14:36

score 48 · Answer 12 · 2026-04-10 18:10:45

48

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Question about three lines theorem

Published on 10 Apr 2026 - 18:10

score 97 · Answer 13 · 2026-05-11 08:29:40

97

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Can the natural logarithm be meaningfully "natural" in the category theory sense?

Published on 11 May 2026 - 8:29

score 82 · Answer 14 · 2026-04-09 11:33:29

82

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Tricky integral involving Arctan

Published on 09 Apr 2026 - 11:33

score 44 · Answer 15 · 2026-04-12 12:07:01

44

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Need help naming a fractal/image generated by exponential

Published on 12 Apr 2026 - 12:07

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$\log_{2} \frac{1-ab}{a + b} = 2ab + a + b -3$. Find min of $(a +b)$

How Can Solving $\left( 2n \right)^{\left( \log_b 2 \right)} = \left( 5n \right)^{\left( \log_b 5 \right)}$ be Generalized for any Base of $\log_b n$?

$\log_a 10 + \log_b 10 +\ log_c 10 \ge \sqrt{3 \log_a 10 * \log_b 10 * \log_c 10}$

Solve $x^2-2x+1=\log_2( \frac{x+1}{x^2+1})$

does Integrating both sides of an equation in dx will Invalidates the equality?

Logarithmic equation: $\log_2 (\frac{x+1}{x^2+2} )= x^2-2x-1$

Show that if $x>1$, $\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-\dfrac{1}{4x^4}-\dfrac{1}{6x^6}-\cdots$

Prove that if $\alpha \geq1$ and $n\geq 2\alpha \log(2\alpha)$ then $n \geq \alpha \log(2n)$

Question about three lines theorem

Can the natural logarithm be meaningfully "natural" in the category theory sense?

Tricky integral involving Arctan

Need help naming a fractal/image generated by exponential

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