Why is it assumed that logarithms are base 10?

Question

Unless already stated? My math teacher went into an explantion but I didn't really get it, maybe you people can explain better?

Also, what does the "laun" button mean on my calculator (it looks like "Ln")? My math teacher said it is has something to do with logs but I don't know exactly.

Answer 1

Main reason is when the monks that figured out logarithms to work exceeding large numbers did it they use the standard numbering system. 0-10. They were after a way to make working problems with exceedingly large numbers easier.

They were doing it out of necessity more than anything else. Hence they use standard 0-10 base numbering system.

That is why unless it is to some other base an 10 it is just stated like this log 100 = ? or something like that.
Log to base ten is the basis for all logarithms.

like log100 = ?
log 100 = 2: what that means is 10 raised to the second power (squared) is 100.

log 50 = 1.69897: What that means is 10 raised to the 1.6987 power is equal to 50.

Just glad I didn't have to figure all that out. It took them a while I'll bet.

You forget there were no computers, there were no calcutators, there were not adding machines back then. All math was done long hand.

Ln has to do with natural logs because it was devised to explain natural occurances in nature and science. Like population growth or decay. . It is based on 2.718281
A lot of times you will see a simply e. or e^ and ln on your calculators depending on their make and model.

such as the natural log of 45.
log e 45 = 3.80666
and the antiog base e of 3.80666

ln 3.30666= 45.

Hope that helps. understand where logs came from.

Answer 2

Logarithms are exponents that are relative to a given base. Calculations involving multiplication, division, raising to powers and extraction of roots can usually be carried out more easily with the use of logarithms. Logarithms contain three parts: the number, the base, and the logarithm. In the following logarithm example, the number is 1000, the base is 10 and the logarithm is 3.

"e" is a numerical constant that is equal to 2.71828. Just as pi (3.14159) is a numerical constant that occurs whenever the circumference of a circle is divided by its diameter. The value of "e" is found in many mathematical formulas such as those describing a nonlinear increase or decrease such as growth or decay (including compound interest), the statistical "bell curve," the shape of a hanging cable or a standing arch. "e" also shows up in some problems of probability, some counting problems, and even the study of the distribution of prime numbers. In the field of nondestructive evaluation it is found in formulas such as those used to describe ultrasound attenuation in a material. The sound energy decays as it moves away from the sound source by a factor that is relative to "e." Because it occurs naturally with some frequency in the world, "e" is used as the base of natural logarithms.

e is usually defined by the following equation:

e = limn->infinity (1 + 1/n)n.

Its value is approximately 2.718 and has been calculated to 869,894,101 decimal places by Sebastian Wedeniwski. The number e was first studied by the Swiss mathematician Leonhard Euler in the 1720s, although its existence was more or less implied in the work of John Napier, the inventor of logarithms, in 1614. Euler was also the first to use the letter e for it in 1727 (the fact that it is the first letter of his surname is coincidental). As a result, sometimes e is called the Euler Number, the Eulerian Number, or Napier's Constant. It was proven by Euler that "e" is an irrational number, so its decimal expansion never terminates, nor is it ever periodic.

An effective way to calculate the value of e is not to use the defining equation above, but to use
the following infinite sum:

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ...

As an example, here is the computation of e to 22 decimal places:

1/0! = 1/1 = 1.0000000000000000000000000
1/1! = 1/1 = 1.0000000000000000000000000
1/2! = 1/2 = 0.5000000000000000000000000
1/3! = 1/6 = 0.1666666666666666666666667
1/4! = 1/24 = 0.0416666666666666666666667
1/5! = 1/120 = 0.0083333333333333333333333
1/6! = 1/720 = 0.0013888888888888888888889
1/7! = 1/5040 = 0.0001984126984126984126984
1/8! = 1/40320 = 0.0000248015873015873015873
1/9! = 1/362880 = 0.0000027557319223985890653
1/10! = 1/3628800 = 0.0000002755731922398589065
1/11! = 1/39916800
= 0.0000000250521083854417188
1/12! = 1/479001600
= 0.0000000020876756987868099
1/13! = 1/6227020800
= 0.0000000001605904383682161
1/14! = 1/87178291200
= 0.0000000000114707455977297
1/15! = 1/1307674368000
= 0.0000000000007647163731820
1/16! = 1/20922789887989
= 0.0000000000000477947733239
1/17! = 1/355687428101759
= 0.0000000000000028114572543
1/18! = 1/6402373705148490
= 0.0000000000000001561920697
1/19! = 1/121645101098757000
= 0.0000000000000000082206352
1/20! = 1/2432901785214670000
= 0.0000000000000000004110318
1/21! = 1/51091049359062800000
= 0.0000000000000000000195729
1/22! = 1/1123974373384290000000
= 0.0000000000000000000008897
1/23! = 1/25839793281653700000000
= 0.0000000000000000000000387
1/24! = 1/625000000000000000000000
= 0.0000000000000000000000016
1/25! = 1/10000000000000000000000000
= 0.0000000000000000000000001


The sum of the values in the right column is 2.7182818284590452353602875 which is "e."



There are two types of logarithms that appear most often. The first type has a base of ten like the example. The second type has a base of e where e ~ 2.718. Since these logarithms appear so often, they are abbreviated. For a logarithm with a base of 10, the base is not written and it is assumed. For a logarithm with a base of e, it is abbreviated to ln, also with no written base.

It is possible to change the base of a logarithm. This is helpful when using bases that are not the two most common bases. This makes it possible to change the base of the logarithm so that it can be calculated using a calculator since most calculators only have the two bases.

Answer 3

Because "log" means "base 10". "ln" means "base e". Other than that, you have to put a little subscript number after "log" to tell what base it's in.

Would you put a subscript "10" after every decimal number? No. Base 10 is the default for a lot of human mathematics. This is just the way it is.

Answer 4

Hi,

logs are assumed to be base 10 unless otherwise stated b/c we generally operate in base 10, but logs can be in any base you choose.

Ln, for example, is the "natural logarithm" -- which is log to the base "e"
e =~ 2.71828...

Check the link.

hth.

REgards,
Chas.

Answer 5

logarithms are not all base ten.
log 10 is log to base ten
log 2 """""""""""""""""""two
log 3"""""""""""""""""""three
etc

ln, log n, is called "Natural LOG" and is a special log.
It is log to base e where e is a special number whose value is approx. 2.718.
This number is widely used in Physics and branches of Engineering.
ln will be that button on your calculator.
Check that ln 2.718 = 1