Log和Ln之间的区别
Log 和 Ln 分别代表对数和自然对数。对数对于求解未知变量作为某个其他量的指数的方程是必不可少的。它们在数学和科学学科的许多分支中都很重要，用于解决涉及复利的问题，复利与金融和经济学广泛相关。
Log 以 10 为底定义，而 ln 以 e 为底定义。示例 - 以 2 为底的对数被写为 log 2 ，而以 e 为底的对数被表示为 log e = ln（自然对数）。
定义为以 e 为底的幂的对数，称为自然对数的对数。 'e' 是指数函数。
日志的定义
数学中的对数是取幂的反函数。换句话说，日志被定义为一个数字必须提高到的幂，以便我们得到另一个数字。这也称为以 10 为底的对数或常用对数。对数的一般形式是：
记录a (y) = x
它也写为
一个x = y
对数的性质
- 日志b (mn)= log b m + log b n
- Log b (m/n)= log b m – log b n
- 日志b (mn) = n log b m
- Log b m = log a m/log a b
ln的定义
Ln 称为自然对数。它也称为以 e 为底的对数。这里，常数e表示一个数，它是一个超越数和一个无理数，大约等于值2.71828182845。自然对数 (ln) 可以表示为 ln x 或 log e x。
Log 和 Ln 的区别
要解决对数问题，必须知道对数和自然对数之间的区别。对指数函数有一个关键的理解也有助于理解不同的概念。下面以表格形式给出了对数和自然对数之间的一些重要区别： log ln 1. Log generally refers to a logarithm to the base 10 Ln generally refers to a logarithm to the base e 2. Also known as the common logarithm Also called the natural logarithm 3. The common log is represented as log10 (x) The natural log is represented as loge (x) 4. The exponential form for this log is 10x = y It has the exponential form as ex=y 5. The interrogative statement for the common logarithm is “At which number should we raise 10 to get y?” The interrogative statement for the natural logarithm is “At which number should we raise Euler’s constant number to get y?” 6. It is mostly used in physics as compared to ln It has much less use in physics 7. It is Represented as log base 10 in maths This is represented as log base e.
示例问题
问题 1. 求解 a in log₂ a = 5
解决方案：
The logarithm function of the above function can be written as 25=a
Therefore, 25= 2 x 2 x 2 x 2 x 2 x 2=32 or y = 32
问题 2. 简化 log(75)。
解决方案：
We will use the Log and ln rules we have discussed. Since we know that the number 75 is not a power of 10 (the way that 100 was), So we can find the value by plugging this into a calculator, remembering to use the “LOG” key (not the “LN” key), and we get
log(75) = 1.87506126339 or log(75) = 1.87 rounded to two decimal places.