The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln( x ) around the z -axis . In mathematics , a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers .

2020年9月11日 · $$\log(z) = \log(\rho)+i(\theta +2k\pi),$$ where $z = \rho e^{i\theta}.$ When $z = i$, then $z = e^{i\frac{pi}{2}}$. Hence, $\rho = 1$ and $\theta = \frac{\pi}{2}$. Finally: $$\log(i) = \log(1) + i \left(\frac{\pi}{2} + 2k \pi\right) = \frac{i\pi}{2}(1 + 4k). $$

In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 103 = 10 × 10 × 10.

On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number. Example: log(1000) = log 10 (1000) = 3

2024年4月30日 · The complex logarithm is an extension of the concept of logarithmic functions involving complex numbers (represented by log z). Mathematically, written as log(z) = log(r ⋅ e iθ ) = ln(r) + i(θ + 2nℼ)

The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. log b (x ∙ y) = log b (x) + log b (y) For example: log 10 (3 ∙ 7) = log 10 (3) + log 10 (7) Logarithm quotient rule. The logarithm of the division of x and y is the difference of logarithm of x and logarithm of y. log b (x / y) = log b (x) - log ...

对数函数（Logarithmic Function）是以 幂 （真数）为自变量，指数为因变量，底数为常量的函数。 对数函数是6类 基本初等函数 之一。 其中对数的定义： 如果a x =N（a>0，且a≠1），那么数x叫做以a为底N的对数，记作x=logaN，读作以a为底N的对数，其中a叫做对数的 底数，N叫做 真数。 一般地，函数y=logaX（a>0，且a≠1）叫做对数函数，也就是说以幂（真数）为自变量，指数为因变量，底数为常量的函数，叫对数函数。 其中x是自变量，函数的 定义域 是（0，+∞）， …

2024年12月30日 · The logarithm is the exponent or power to which a base is raised to get a particular number. For example, 'a' is the logarithm of 'm' to the base of 'x' if xm = a, then we can write it as m = logxa. Logarithms are invented to speed up the calculations and time will be reduced when we are multiplying

2021年10月18日 · 对数公式是数学中的一种常见公式，如果a^x=N(a>0,且a≠1)，则x叫做以a为底N的对数,记做x=log(a)(N)，其中a要写于log右下。 其中a叫做对数的底，N叫做真数 。

2021年8月11日 · The principal value of \(log\,z\) is the value obtained from equation (2) when \(n=0\) and is denoted by \(Log\,z\). Thus \(Log\,z=ln\,r+i\Theta \). The function \(Log\,z\) is well defined and single-valued when \(z≠0\) and that \(log\,z=Log\,z+2n\pi i\,\,\,\left ( …