# Questions tagged [logarithm]

In mathematics, the logarithm is the inverse function to exponentiation.

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### Can I find the number e in the tables of Napier?

As Napier calculated the logarithms of numbers in the base $\left(1-\frac{1}{10^7}\right)^{10^7}$, I expected to find the number $e$ in the tables of his Mirifici Logarithmorum Canonis Descriptio. ...
• 111
239 views

### How did mathematics come to use $\log(x)$ and not $\ln(x)$

Question: How and why did the discipline of mathematics come to use $\log(x)$ and not $\ln(x)$ in its writing - papers, books, teaching? Clearly $\ln(x)$ is unambiguously $\log_e(x)$, but $\log(x)$ is ...
• 365
103 views

### Did the logarithm function, with a continuous domain, come before the exponential function? [duplicate]

I was digging about the discovery of logarithms by John Napier. It is clear that he was looking for a function he could compute (at least approximately) that would map products into sums. He came up ...
• 111
95 views

### Did anyone ever propose an analytic definition of zero divisors, including nilpotents, as opposed to algebraic definition?

I wonder, can we meaningfully define zero divisors based on analytic rather than algebraic approach? For instance, if we extend the real numbers with divergent integrals and series, and evaluate the ...
• 642
75 views

### Historically, was logarithmic function ever used to determine anything other than direction and scale of a vector?

In nearly all areas of mathematics, logarithmic function applied to various objects where it is defined, produces either direction data or scale data of the object. Are there any examples of ...
• 642
324 views

### Why did John Napier use logós ‘ratio’, to coin "logarithm"?

I agree that logarithms are numbers, and Napier chose arithmós reasonably. But why did Napier pick Greek logós ‘ratio’? I don't see a ratio in this definition of the logarithm in James Stewart, ...
1 vote
176 views

### What astronomy efforts required multiplication of large numbers around 1600?

I'm reading an article about the history of logarithms and it says: One problem that was plaguing people at the time, especially astronomers, was arithmetic. Astronomical calculations required the ...
• 291
911 views

### Who was the first person to notice logarithms of negatives numbers and for what reason?

Who was the first person to notice logarithms of negatives numbers and why? When did they first arise naturally? I thought I saw somewhere that it had to do with integration but I can't find it ...
471 views

### How does Charles Babbage's Difference Engine solve his quest for automating Log Tables?

At the London Science Museum, we see a model built in 1999 of Charles Babbage's Difference Engine No.2 based on the plans he left: We know that Charles Babbage wrote a book of log tables: In doing ...
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