### 计算机代写|计算机图形学作业代写computer graphics代考|Laws of Indices

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|计算机图形学作业代写computer graphics代考|Laws of Indices

The laws of indices are expressed as follows:
\begin{aligned} a^{m} \times a^{n} &=a^{m+n} \ \frac{a^{m}}{a^{n}} &=a^{m-n} \ \left(a^{m}\right)^{n} &=a^{m n} \end{aligned}
and are verified using some simple examples:
\begin{aligned} 2^{3} \times 2^{2} &=2^{5}=32 \ \frac{2^{4}}{2^{2}} &=2^{2}=4 \ \left(2^{2}\right)^{3} &=2^{6}=64 \end{aligned}
From the above laws, it is evident that
\begin{aligned} a^{0} &=1 \ a^{-p} &=\frac{1}{a^{p}} \ a^{\frac{1}{4}} &=\sqrt[q]{a} \ a^{\frac{2}{q}} &=\sqrt[4]{a^{p}} . \end{aligned}

## 计算机代写|计算机图形学作业代写computer graphics代考|Logarithms

Two people are associated with the invention of logarithms: the Scottish theologian and mathematician John Napier (1550-1617), and the Swiss clockmaker and mathematician Joost Bürgi (1552-1632). Both men were frustrated by the time they spent multiplying numbers together, and both realised that multiplication could be replaced by addition using logarithms. Logarithms exploit the addition and subtraction of indices shown above, and are always associated with a base. For example, if $a^{x}=n$, then $\log _{a} n=x$, where $a$ is the base. Where no base is indicated, it is assumed to be 10 . Two examples bring the idea to life:
$$\begin{array}{rll} 10^{2}=100 & \text { then } & \log 100=2 \ 10^{3}=1000 & \text { then } & \log 1000=3 \end{array}$$
which is interpreted as ‘ 10 has to be raised to the power (index) 2 to equal 100.’ The log operation finds the power of the base for a given number. Thus a multiplication

is translated into an addition using logs. Figure $3.3$ shows the graph of $\log x$, up to $x=100$, where we see that $\log 20 \approx 1.3$ and $\log 50 \approx 1.7$. Therefore, given suitable software, logarithm tables, or a calculator with a log function, we can compute the product $20 \times 50$ as follows:
\begin{aligned} \log (20 \times 50)=\log 20+\log 50 & \approx 1.3+1.7=3 \ 10^{3} &=1000 \end{aligned}
In general, the two bases used in calculators and software are 10 and $e=2.718281846 \ldots$. To distinguish one type of logarithm from the other, a logarithm to the base 10 is written as log, and a natural logarithm to the base $e$ is written $\ln$.
Figure $3.4$ shows the graph of $\ln x$, up to $x=100$, where we see that $\ln 20 \approx 3$ and $\ln 50 \approx 3.9$. Therefore, given suitable software, a set of natural logarithm tables or a calculator with a $\ln$ function, we can compute the product $20 \times 50$ as follows:
\begin{aligned} \ln (20 \times 50)=\ln 20+\ln 50 & \approx 3+3.9=6.9 \ e^{6.9} & \approx 1000 \end{aligned}

## 计算机代写|计算机图形学作业代写computer graphics代考|Further Notation

All sorts of symbols are used to stand in for natural language expressions; here are some examples:
$<$ less than $>$ greater than
$\leq$ less than or equal to
$\geq$ greater than or equal to
$\approx$ approximately equal to
$\equiv$ equivalent to

• not equal to
$|x|$ absolute value of $x$.
For example, $0 \leq t \leq 1$ is interpreted as: $t$ is greater than or equal to 0 , and is less than or equal to 1 . Basically, this means $t$ varies between 0 and 1 .

## 计算机代写|计算机图形学作业代写computer graphics代考|Laws of Indices

23×22=25=32 2422=22=4 (22)3=26=64

## 计算机代写|计算机图形学作业代写computer graphics代考|Logarithms

102=100 然后 日志⁡100=2 103=1000 然后 日志⁡1000=3

ln⁡(20×50)=ln⁡20+ln⁡50≈3+3.9=6.9 和6.9≈1000

## 计算机代写|计算机图形学作业代写computer graphics代考|Further Notation

<少于>比…更棒
≤小于或等于
≥大于或等于
≈大约等于
≡相当于

• 不等于
|X|的绝对值X.
例如，0≤吨≤1被解释为：吨大于或等于 0 ，并且小于或等于 1 。基本上，这意味着吨在 0 和 1 之间变化。

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。