Windows 7计算器的对数计算 [英] Logarithm Calculation with Windows 7 Calculator

问题描述

我想在科学模式下使用 Windows计算器来求解一个非常基本的对数方程，但是很遗憾，我不能这样做.

I would like to use the Windows Calculator in Scientific Mode in order solve a very basic Logarithm equation but, unfortunately, I couldn't do that.

问题出在这里

log_5 125=?

非常感谢您的帮助...

Thank you very much for your help...

好吧，我知道它等于"3"，但是，例如，如何使用Windows计算器来计算该等式?

Well, I know it equals to "3", but, how can I use the Windows Calculator to get computed that equation for example?

推荐答案

您可以通过使用以下等式计算任意基数中的两个对数来计算给定基数中的对数:

You can calculate a logarithm in a given base by calculating two logarithms in an arbitrary base, using the following equation:

log_b (x) = log_k (x) / log_k (b)

随着Windows计算器出现一个ln按钮，该按钮代表自然对数(即，以e为基础登录)，则可以按125，ln，/，5，ln，以获得所需的结果.

As the windows calculator got a ln button, which stands for the natural logarithm (that is, log in basis e,) then you can press 125, ln, /, 5, ln, and get the desired result.

对于奖励积分，这是上述方程式成立的原因:

For bonus points, here is why the above equation holds:

• 让a ^b = c.请记住，这将设置b = log_a(c).
• 取第一个等式两边的log_k.我们得到:log_k(a ^b )= log_k(c)
• 使用对数身份日志(x ^y )= y * log(x)，我们得到b * log_k(a)= log_k(c)
• 因此b = log_k(c)/log_k(a).
• 从第一步开始，我们有b = log_a(c)，因此log_a(c)= log_k(c)/log_k(a). QED.

• Let a^b = c. Remember that this sets b = log_a (c).
• Take log_k of both sides of the first equation. We get: log_k (a^b) = log_k (c)
• Using the logarithmic identity log (x^y) = y * log (x), we get b * log_k (a) = log_k (c)
• Hence b = log_k (c) / log_k (a).
• From the first step, we have b = log_a (c), hence log_a (c) = log_k (c) / log_k (a). QED.

这篇关于Windows 7计算器的对数计算的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！