# logarithm function

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##### 2: 4.2 Definitions
###### §4.2(i) The Logarithm
The general logarithm function $\operatorname{Ln}z$ is defined by …
###### §4.2(ii) Logarithms to a General Base $a$
Natural logarithms have as base the unique positive number …
##### 5: 5.10 Continued Fractions
###### §5.10 Continued Fractions
5.10.1 $\operatorname{Ln}\Gamma\left(z\right)+z-\left(z-\tfrac{1}{2}\right)\ln z-% \tfrac{1}{2}\ln\left(2\pi\right)=\cfrac{a_{0}}{z+\cfrac{a_{1}}{z+\cfrac{a_{2}}% {z+\cfrac{a_{3}}{z+\cfrac{a_{4}}{z+\cfrac{a_{5}}{z+}}}}}}\cdots,$
##### 6: 4.1 Special Notation
 $k,m,n$ integers. …
The main purpose of the present chapter is to extend these definitions and properties to complex arguments $z$. The main functions treated in this chapter are the logarithm $\ln z$, $\operatorname{Ln}z$; the exponential $\exp z$, $e^{z}$; the circular trigonometric (or just trigonometric) functions $\sin z$, $\cos z$, $\tan z$, $\csc z$, $\sec z$, $\cot z$; the inverse trigonometric functions $\operatorname{arcsin}z$, $\operatorname{Arcsin}z$, etc. …
##### 8: 4.8 Identities
###### §4.8(i) Logarithms
4.8.1 $\operatorname{Ln}\left(z_{1}z_{2}\right)=\operatorname{Ln}z_{1}+\operatorname{% Ln}z_{2}.$
4.8.3 $\operatorname{Ln}\frac{z_{1}}{z_{2}}=\operatorname{Ln}z_{1}-\operatorname{Ln}z% _{2},$
4.8.13 $\ln\left(a^{x}\right)=x\ln a,$ $a>0$.
##### 9: 4.3 Graphics Figure 4.3.1: ln ⁡ x and e x . … Magnify
###### §4.3(ii) Complex Arguments: Conformal Maps Figure 4.3.3: ln ⁡ ( x + i ⁢ y ) (principal value). … Magnify 3D Help
##### 10: 5.3 Graphics Figure 5.3.2: ln ⁡ Γ ⁡ ( x ) . … Magnify