Question

The nature of the number $a$ where $\log_p(q)=a$

score 51 · Answer 1 · 2026-03-29 04:10:51

51

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The nature of the number $a$ where $\log_p(q)=a$

Published on 29 Mar 2026 - 4:10

score 3.6k · Answer 2 · 2026-03-25 06:06:54

3.6k

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Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$

Published on 25 Mar 2026 - 6:06

score 881 · Answer 3 · 2026-03-26 10:56:19

881

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Why is $ a^x = e^{x \log a} $?

Published on 26 Mar 2026 - 10:56

score 99 · Answer 4 · 2026-03-26 11:00:18

99

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If $2^a=3^b$ find $\frac{a}{b}$

Published on 26 Mar 2026 - 11:00

score 103 · Answer 5 · 2018-12-25 14:03:08

103

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Solve $\log_{10}{(10^x+100)} = \frac{1}{2}x+1+\log_{10}2$

Published on 25 Dec 2018 - 14:03

score 81 · Answer 6 · 2018-12-25 14:24:13

81

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A problem involving the distance between points on two logarithmic curves

Published on 25 Dec 2018 - 14:24

score 1.3k · Answer 7 · 2018-12-26 02:53:59

1.3k

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How to check for polynomial

Published on 26 Dec 2018 - 2:53

score 1.8k · Answer 8 · 2026-03-25 16:40:16

1.8k

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Why are the local extrema of a log-transformed function equal to local extrema of the original function?

Published on 25 Mar 2026 - 16:40

score 382 · Answer 9 · 2026-03-25 22:05:27

382

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Compute $\sum\limits_{j = 0}^{m - 1} \left(c_j + 1\right)\ln\left(c_j + 1\right)$ where $c_j = \cos\left(\frac{\pi}{2m}\left(1 + 2j\right) \right)$

Published on 25 Mar 2026 - 22:05

score 529 · Answer 10 · 2018-12-28 10:01:03

529

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Evaluating $\int_0^1\arctan x\ln(1+x)\left(\frac2x-\frac3{1+x}\right)dx$

Published on 28 Dec 2018 - 10:01

score 109 · Answer 11 · 2026-03-29 07:22:22

109

Views

Solving a first-order nonlinear ordinary differential equation (for a physics problem)

Published on 29 Mar 2026 - 7:22

score 744 · Answer 12 · 2026-03-26 11:01:04

744

Views

Finding the inverse of my f(x) function that includes a fractional exponent (with a variable in the fraction)

Published on 26 Mar 2026 - 11:01

score 40 · Answer 13 · 2018-12-29 15:58:36

40

Views

How to prove this equation $\log^2_a(x) = \log_a(x^{\log_ax})$?

Published on 29 Dec 2018 - 15:58

score 27 · Answer 14 · 2026-03-26 17:51:56

27

Views

Problem with system of logarythmic equation.

Published on 26 Mar 2026 - 17:51

score 87 · Answer 15 · 2026-03-28 14:53:48

87

Views

Solving an DE involving a logarithm

Published on 28 Mar 2026 - 14:53

List Question

The nature of the number $a$ where $\log_p(q)=a$

Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$

Why is $ a^x = e^{x \log a} $?

If $2^a=3^b$ find $\frac{a}{b}$

Solve $\log_{10}{(10^x+100)} = \frac{1}{2}x+1+\log_{10}2$

A problem involving the distance between points on two logarithmic curves

How to check for polynomial

Why are the local extrema of a log-transformed function equal to local extrema of the original function?

Compute $\sum\limits_{j = 0}^{m - 1} \left(c_j + 1\right)\ln\left(c_j + 1\right)$ where $c_j = \cos\left(\frac{\pi}{2m}\left(1 + 2j\right) \right)$

Evaluating $\int_0^1\arctan x\ln(1+x)\left(\frac2x-\frac3{1+x}\right)dx$

Solving a first-order nonlinear ordinary differential equation (for a physics problem)

Finding the inverse of my f(x) function that includes a fractional exponent (with a variable in the fraction)

How to prove this equation $\log^2_a(x) = \log_a(x^{\log_ax})$?

Problem with system of logarythmic equation.

Solving an DE involving a logarithm

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