New posts in logarithms

A closed form for $\int_0^\infty\ln x\cdot\ln\left(1+\frac1{2\cosh x}\right)dx$

calculus integration logarithms improper-integrals closed-form

Integral $\int_0^{\pi/2}\frac{x}{\sin x}\log^2\left(\frac{1+\cos x-\sin x}{1+\cos x+\sin x}\right)dx$

calculus integration trigonometry definite-integrals logarithms

Need help with $\int_0^\infty e^{-x}\ln\ln\left(e^x+\sqrt{e^{2x}-1}\right)\,dx$

calculus integration logarithms improper-integrals closed-form

How did the notation "ln" for "log base e" become so pervasive?

notation logarithms math-history

Integral $\int_0^\infty\frac{1}{\sqrt[3]{x}}\left(1+\log\frac{1+e^{x-1}}{1+e^x}\right)dx$

calculus integration definite-integrals logarithms closed-form

How to type logarithms in Wolfram|Alpha?

logarithms wolfram-alpha

Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$

integration trigonometry definite-integrals logarithms polylogarithm

How does the simplification of the absolute value logarithm work?

integration logarithms

Why aren't logarithms defined for negative $x$?

number-theory logarithms definition

An alternative way to calculate $\log(x)$

numerical-methods logarithms

Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

real-analysis inequality summation logarithms contest-math

The difference between log and ln

logarithms

Evaluating $\int_0^\pi\arctan\bigl(\frac{\ln\sin x}{x}\bigr)\mathrm{d}x$

calculus integration definite-integrals logarithms closed-form

Closed form for $\int_0^1\sqrt{\frac{2-x}{(1-x)\,x}}\,\log\left(\frac{(2-x)\,x}{1-x}\right)dx$

calculus integration definite-integrals logarithms closed-form

Underlying Reason For Taking Log Base 10

algebra-precalculus logarithms exponentiation

Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$

limits logarithms limits-without-lhopital

limit of a $\ln(\cos(x))/x$ [closed]

calculus limits trigonometry logarithms

Is $\log(z^2)=2\log(z)$ if $\text{Log}(z_1 z_2)\ne \text{Log}(z_1)+\text{Log}(z_2)$?

complex-analysis logarithms multivalued-functions

Integral $\int_0^1\frac{\ln x}{\left(1+x\right)\left(1+x^{-\left(2+\sqrt3\right)}\right)}dx$

calculus integration definite-integrals logarithms closed-form

Integral $\int_0^1\ln\ln\,_3F_2\left(\frac{1}{4},\frac{1}{2},\frac{3}{4};\frac{2}{3},\frac{4}{3};x\right)\,dx$

calculus integration logarithms closed-form hypergeometric-function