Explore: Log Sin

log ⁡ 2 π 2 n + 1 2 { log ⁡ π − log ⁡ sin ⁡ π k n } + 1 π ∑ r = 1 n − 1 γ + log ⁡ r r ⋅ sin ⁡ 2 π r k n − 1 2 π sin ⁡ 2 π k n ⋅ ∫ 0 ∞ e − n x ⋅ log ⁡

⁡ ( φ ) = − ∫ 0 φ log ⁡ | 2 sin ⁡ x 2 | d x : {\displaystyle \operatorname {Cl} _{2}(\varphi )=-\int _{0}^{\varphi }\log \left|2\sin {\frac {x}{2}}\right|\

\exp } ), the natural logarithm ( log {\displaystyle \log } ), trigonometric functions ( sin , cos {\displaystyle \sin ,\cos } ), and their inverses. The

= z log ⁡ ( sin ⁡ π z ) − ∫ 0 z log ⁡ ( sin ⁡ π x ) d x = z log ⁡ ( sin ⁡ π z ) − ∫ 0 z [ log ⁡ ( 2 sin ⁡ π x ) − log ⁡ 2 ] d x = z log ⁡ ( 2 sin ⁡ π

⁡ sin ⁡ [ φ 2 + exp ⁡ [ log ⁡ sin ⁡ [ φ 1 ] + A 1 ] ] + A 2 ] {\displaystyle \exp[\log \sin[\varphi _{2}+\exp[\log \sin[\varphi _{1}]+A_{1}]]+A_{2}]}

subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations

formula: log b ⁡ x = log 10 ⁡ x log 10 ⁡ b = log e ⁡ x log e ⁡ b . {\displaystyle \log _{b}x={\frac {\log _{10}x}{\log _{10}b}}={\frac {\log _{e}x}{\log _{e}b}}

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally

In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for

formula: log b ⁡ ( x ) = log 10 ⁡ ( x ) log 10 ⁡ ( b ) = log e ⁡ ( x ) log e ⁡ ( b ) . {\displaystyle \log _{b}(x)={\frac {\log _{10}(x)}{\log _{10}(b)}}={\frac