Logarithm Definition

Noun

Singular logarithm

Plural logarithms

logarithm (plural logarithms)

  1. (mathematics) For a number x, the power to which a given base number must be raised in order to obtain x. Written logbx. For example, log101000 = 3 because 10 = 1000.

From Wiktionary under the GNU Free Documentation License.
Sun Jul 12 02:32:50 2009

Logarithm Facts

In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.

For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 10 = 1000, so log101000 = 3, and 2 = 32, so log232 = 5.

The logarithm of x to the base b is written logb(x) or, if the base is implicit, as log(x). So, for a number x, a base b and an exponent y,

An important feature of logarithms is that they reduce multiplication to addition, by the formula:

That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers. The use of logarithms to facilitate complicated calculations was a significant motivation in their original development.

From Wikipedia under the GNU Free Documentation License
Mon Jul 6 02:08:27 2009

Logarithm Answers
Explain the difference between a logarithm of a product and the product of logarithms ?
Q. Explain the difference between a logarithm of a product and the product of logarithms and give examples of each.
Asked by Amy S - Mon Dec 8 17:30:52 2008 - - 3 Answers - 0 Comments
Can anyone explain the difference between the logarithm of a product and the product of logarithms?
Q. Logarithms really confuse me. I need help :)
Asked by pickymom - Mon Nov 17 19:49:03 2008 - - 1 Answers - 0 Comments
How do I prove a logarithm with a power for the base?
Q. I have: log(base b^n) of x = 1/n log(base b) of x How do I prove this? *Note* I'm only a 9th grader. Also list for each step what property was used/ axiom.
Asked by 1234 - Sat Nov 22 17:00:55 2008 - - 1 Answers - 0 Comments

A. Theorem 1) log(base a) of x = log(x) / log(a) where the last two logs can be of any base. Lemma 1) log(base b^n) of x = log(x) / log(b^n)...any base Theorem 2) log(b^n) = n*log(b)...This is true for any base. Therefore: log(base b^n) of x = n * log (base b) of x By Lemma (1): log(base b^n) of x = log(base b) of x / log(base b) of b^n = log(base b) of x / [n * log(base b) of b] and since log(base b) of b = 1 it is equal to: [log(base b) of x] / n...End Proof .
Answered by Gerry - Sat Nov 22 20:20:25 2008

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Mon Jul 27 21:46:55 2009

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Logarithm Blogs
UNsolved problem 198525 added to logarithm
algebra.com
UNsolved problem 198525 added to logarithm



Mon, 01 Jun 2009 04:50:36 GM

Click on the link to solve this problem: Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of ...

Matrix logarithm mistake?
physicsforums.com
Matrix logarithm mistake?

farleyknight

ue, 26 May 2009 21:23:34 GM

If I'm not mistaken, it supposed to be a generalization of the . logarithmic. function for real numbers: So I might try out this function and hand that in, telling him the corrected ...

UNsolved problem 193127 added to logarithm
algebra.com
UNsolved problem 193127 added to logarithm



Sun, 26 Apr 2009 08:56:07 GM

Click on the link to solve this problem: Hello Tutor, This problem is confusing me. 4^x+5=e^5x The directions is to solve. We are in a chapter of . logarithm. . Please help!

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Mon Jul 13 04:37:19 2009