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ln(x) vs log(x) on wolfram alpha?
Ive noticed that on WolframAlpha that every time I type a function with ln(*), the website changes it to log(*). I know these functions are similar but can they really be treated interchangeably this way?
5 Answers
- 5 years ago
Ln(x) is Log(x) with base of e^1. When you're integrating ln(x), you're really integrating a form of Log. So the answers Wolfram gives should be treated as log with base e^1. Though I admit it's a really uncomfortable way of representing the integral. A calculator that does not do that is http://www.integral-calculator.com/
- Randy PLv 75 years ago
log(x) in most computer languages stands for the natural log, i.e. ln. That includes Mathematica, the language that is "under the hood" at Wolfram Alpha.
https://reference.wolfram.com/language/ref/Log.htm...
The base-10 log is almost always represented as log10(x).
There are also many textbooks that choose to use "log" as standing for the natural log, especially in physics where the base-10 log is hardly ever useful.
- Anonymous5 years ago
It changes it, but it also says "log(x) is the natural logarithm" so it's merely changing the spelling, not changing the function.
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- 5 years ago
Wolframalpha treats log(x) as ln(x) and not as the common logarithm. You have to explicitly tell it when you mean natural logarithm or common logarithm.
But, the change of base formula can relate ln(x) to log(x)
ln(x) => log[e](x)
log(x) => log[10](x)
log[a](b) => log[c](b) / log[c](a)
log[10](x) =>
log[e](x) / log[e](10) =>
ln(x) / ln(10)
Therefore
log(x) = ln(x) / ln(10)
