logarithm

简明释义

英[ˈlɒɡərɪðəm]美[ˈlɔːɡərɪðəm]

n. [数] 对数

英英释义

单词用法

同义词

反义词

例句

1.An estimated logarithm of parameter with good stability and quick convergence BFGS logarithm is suggested.

提出一种稳定性好、收敛速度快的参数估计算法——BFGS算法。

2.Replaces the current quaternion with its natural logarithm.

用当前四元数的自然对数替换此四元数。

3.According to the model, limen of logarithm loudness is independent of intensity.

这个模型认为，响度对数的辨别阈不随信号强度变化。

4.The fifth day is the logarithm stage for the mycelium growth.

菌丝体生长的第五天为菌丝对数生长阶段。

5.If we use exponentiation to encrypt or decrypt, the adversary can use logarithm to attack.

如果我们运用求幂运算来加密和解密，对手就可以运用对数进行攻击。

6.Both of their security are based on the intractability of elliptic curve discrete logarithm problem.

两种方案的安全性都是基于椭圆曲线离散对数问题的难解性。

7.The results indicate depentence of the film dissolution pn the ionic defect. The, film dissolution obeys the logarithm law.

结果表明：钛氧化膜的溶解和膜中存在离子缺陷有关，膜溶解遵从对数规律。

8.In mathematics, the base-10 logarithm is often used in scientific calculations.

在数学中，常用的以10为底的对数常用于科学计算。

9.The formula to calculate the logarithm of a number is essential in algebra.

计算一个数字的对数的公式在代数中是必不可少的。

10.When analyzing data, we sometimes take the logarithm to simplify the relationships between variables.

在分析数据时，我们有时会取对数来简化变量之间的关系。

11.The natural logarithm is denoted as ln(x) and has many applications in calculus.

自然对数用ln(x)表示，在微积分中有许多应用。

12.Understanding the properties of logarithms is crucial for solving exponential equations.

理解对数的性质对于解决指数方程至关重要。

作文

Understanding the concept of logarithm is crucial for students who wish to delve into the world of mathematics and its applications. A logarithm, defined as the exponent by which a base must be raised to produce a given number, serves as a fundamental tool in various fields such as science, engineering, and finance. For instance, in the expression log_b(a) = c, 'b' is the base, 'a' is the number, and 'c' is the logarithm. This equation means that b raised to the power of c equals a. Understanding this relationship can help simplify complex calculations, especially when dealing with exponential growth or decay. One of the most significant applications of logarithm is in solving exponential equations. For example, in population studies, researchers often use logarithms to model growth rates. If a population doubles every year, using logarithms allows us to calculate the time it will take for the population to reach a certain size. This is particularly useful in predicting future trends and making informed decisions based on data. Additionally, in finance, logarithms are used to calculate compound interest, helping investors understand how their money will grow over time. Moreover, logarithms play a critical role in computer science, particularly in algorithms and data structures. Many algorithms, such as binary search, rely on logarithmic time complexity, which means that the time taken to perform an operation increases logarithmically as the size of the input data increases. This efficiency is vital for handling large datasets, making logarithms an essential concept for aspiring programmers and data scientists. In addition to practical applications, the historical context of logarithms also adds depth to our understanding. The invention of logarithms in the early 17th century by John Napier revolutionized mathematics by simplifying calculations that were previously tedious and time-consuming. Before calculators and computers, mathematicians relied on logarithmic tables to perform multiplication and division through addition and subtraction of logarithms. This innovation not only increased efficiency but also paved the way for advancements in navigation, astronomy, and engineering. In conclusion, mastering the concept of logarithm is essential for anyone pursuing studies in mathematics or related fields. Its applications across various domains highlight its importance in both theoretical and practical scenarios. By understanding how to manipulate and apply logarithms, students can unlock new ways of thinking about problems and enhance their analytical skills. As we continue to explore the vast landscape of mathematics, logarithms will undoubtedly remain a key component in our toolkit, enabling us to tackle complex challenges with confidence. Therefore, embracing the study of logarithms not only enriches our knowledge but also equips us with the skills necessary to navigate an increasingly data-driven world.

理解对数的概念对于希望深入数学及其应用领域的学生至关重要。对数被定义为一个基数必须提升到多大才能产生一个给定数字，它是科学、工程和金融等多个领域的基本工具。例如，在表达式log_b(a) = c中，'b'是基数，'a'是数字，而'c'是对数。这个方程意味着b的c次方等于a。理解这种关系可以帮助简化复杂计算，尤其是在处理指数增长或衰减时。 对数最重要的应用之一是在解决指数方程中。例如，在人口研究中，研究人员经常使用对数来建模增长率。如果一个人口每年翻一番，使用对数可以让我们计算出人口达到某一规模所需的时间。这在预测未来趋势和根据数据做出明智决策时尤为有用。此外，在金融领域，对数被用来计算复利，帮助投资者了解他们的钱会随着时间的推移而如何增长。 此外，对数在计算机科学中也起着关键作用，特别是在算法和数据结构中。许多算法，如二分搜索，依赖于对数时间复杂度，这意味着执行操作所需的时间随着输入数据大小的增加而呈对数增长。这种效率对于处理大型数据集至关重要，使得对数成为有志程序员和数据科学家的重要概念。 除了实际应用外，对数的历史背景也为我们的理解增添了深度。约翰·纳皮尔在17世纪初发明的对数通过简化以前繁琐且耗时的计算而彻底改变了数学。在计算器和计算机出现之前，数学家们依靠对数表通过加法和减法来执行乘法和除法。这一创新不仅提高了效率，还为航海、天文学和工程学的进步铺平了道路。 总之，掌握对数的概念对于任何追求数学或相关领域学习的人来说都是必不可少的。它在各个领域的应用突显了其在理论和实际场景中的重要性。通过理解如何操纵和应用对数，学生可以开辟新的思维方式来解决问题，并增强他们的分析能力。随着我们继续探索广阔的数学领域，对数无疑将继续作为我们工具箱中的关键组成部分，使我们能够自信地应对复杂挑战。因此，接受对数的学习不仅丰富了我们的知识，也为我们提供了在日益数据驱动的世界中航行所需的技能。