Linked Questions

2
votes
0answers
149 views

What did “logarithm” initially mean? [duplicate]

I just read that logarithms were not initially defined in terms of their inverse relationship to exponential functions (and that Euler was the first to develop them in this way). So how were they ...
0
votes
0answers
32 views

Motivation for logarithmic function [duplicate]

What was John Napier's motivation to introduce the logarithmic function? It neither makes the calculations easier nor accurate (at least for me). How could people think of its importance even before ...
19
votes
6answers
18k views

Calculate logarithms by hand

I'm thinking of making a table of logarithms ranging from 100-999 with 5 significant digits. By pen and paper that is. I'm doing this old school. What first came to mind was to use $\log(ab) = \log(a)...
6
votes
3answers
2k views

How popular and used were logarithm tables?

I've heard that, for a time, logarithm tables "sold more than the Bible". Can someone produce some reliable documentation about how prevalent they were ? Would a common shopkeep have one ? Would a ...
16
votes
3answers
3k views

How was the first log table put together?

Henry Briggs compiled the first table of base-$10$ logarithms in 1617, with the help of John Napier. My question is: how did he calculate these logarithms? How were logarithms calculated back then? ...
6
votes
3answers
830 views

How was $e$ first calculated?

I understand how $\pi$ is calculated, but I am interested in references that explain when and how the natural exponent $e$ was developed. What mathematical principles are behind the value of $e$?
4
votes
6answers
518 views

Why can different symmetry groups be isomorphic?

What I understand : A group is characterized by how any two of its elements interact. It is the "structure" of the group that describes it. Thus two groups having the same structure are basically the ...
4
votes
2answers
5k views

How did john Napier make log table [duplicate]

I was just checking the log table and then suddenly It came to my mind that how were log tables made before calculators/computers how did john Napier calculate so precisely the values of $\log(2),\log(...
1
vote
3answers
85 views

What is the intuitive reasoning behind the “change of base” formula in logarithms? [duplicate]

The "change of base" formula in logarithms is: I've seen and I understand each step of the proof, but somehow, when I see the formula as a whole, I fail to grasp it. Why is this true? How do I ...
2
votes
1answer
88 views

History of logarithms and exponentials

A friend and I were discussing the "early transcendentals" terminology used on some calculus books and looked up the phrase, which directed me to this answer: What's the difference between early ...
1
vote
0answers
69 views

Derivation for Napier Logarithm

Something new that I came across called the Napier Logarithm. I was reading the book “Computing: A Historical and Technical Perspective”, and the book says that $$Nap.log x = 10^7(\log_e(10^7/x))$$ I ...
1
vote
1answer
68 views

Geometric definition of logarithm (finite and non-kinematic)

Is there a geometric definition of the logarithm function that is non-kinematic and does not involve an infinite procedure? With base 10, for example. I'm asking for definition, not construction ...