# LOGARITHMS

50 %
50 %
Education

Published on May 25, 2010

Author: manpreet.oberoi2

Source: authorstream.com

LOGARITHMS : LOGARITHMS Slide 2: Logarithms were developed in the 17th century by the Scottish mathematician, John Napier. They were a clever method of reducing long multiplications into much simpler additions (and reducing divisions into subtractions). Slide 3: Young John Napier had to help his dad, who was a tax collector. John got sick of multiplying and dividing large numbers all day and devised logarithms to make his life easier. Slide 4: The use of logarithms made trigonometry and many other fields of mathematics much simpler to calculate. Slide 5: When calculus was developed later in the century, logarithms became central to many solutions. Today, logarithms are still important in many fields of science and engineering, even though we use calculators for most simple calculations. Logarithmic Functions : Logarithmic Functions A logarithm is simply an exponent that is written in a special way. Slide 7: For example, we know that the following exponential equation is true: 32 = 9 In this case, the base is 3 and the exponent is 2. We can write this equation in logarithm form (with identical meaning) as follows: log39 = 2 log39 = 2 : log39 = 2 We say this as "the logarithm of 9 to the base 3 is 2". What we have effectively done is to move the exponent down on to the main line. This was done historically to make multiplications and divisions easier, but logarithms are still very handy in mathematics. Slide 9: The logarithmic function is defined as: f(x) = logbx The base of the logarithm is b. The 2 most common bases that we use are base 10 and base e, which we meet in Logs to base 10 and Natural Logs (base e) in later sections. Slide 10: The logarithmic function has many real-life applications, in acoustics, electronics, earthquake analysis and population prediction. Example 1: Write in logarithm form: 8 = 23 : Example 1: Write in logarithm form: 8 = 23 Solution: log28 = 3 This just follows from the definition of a logarithm. Example 2: Write in exponential form: log101000 = 3 : Example 2: Write in exponential form: log101000 = 3 Solution: 1000 = 103 Once again, this just follows from the definition of a logarithm. Example 3: Find b if : Example 3: Find b if SOLUTION: THANK YOU : THANK YOU

 User name: Comment:

August 22, 2017

August 22, 2017

August 22, 2017

August 22, 2017

August 22, 2017

August 2, 2017

## Related pages

### Logarithm - Wikipedia, the free encyclopedia

Change of base. The logarithm log b (x) can be computed from the logarithms of x and b with respect to an arbitrary base k using the following formula:

### Logarithmus – Wikipedia

binärer Logarithmus, auch als Zweierlogarithmus bezeichnet, der Logarithmus zur Basis 2; er wird in der Informatik bei Rechnungen im Binärsystem verwendet.

### Introduction to Logarithms - Math is Fun - Maths Resources

Common Logarithms: Base 10. Sometimes a logarithm is written without a base, like this: log(100) This usually means that the base is really 10. It is ...

### Logarithmus und Logarithmusgesetze - Formelsammlung Mathe ...

Sieh in dieser übersichtliche Formelsammlung Mathe die wichtigsten Formeln und Erklärungen zum Logarithmus und den Logarithmusgesetzen nach.

### Logarithmus / Logarithmieren ( Berechnen )

Logarithmus zur Basis 2: Zweierlogarithmus. Schauen wir uns noch einmal das Beispiel von eben an: y = 2 x. Diese Gleichung soll nun nach x aufgelöst werden.

### Logarithms - Topics in precalculus - Free Math Courses

The meaning of a logarithm. Common logarithms. Natural logarithms. The three laws of logarithms. Change of base.

### Logarithms - A complete course in algebra - Free Math Courses

The meaning of a logarithm. The three laws of logarithms. Common logarithms.

### Logarithmen und Logarithmusgesetze (Onlinekurs, Übungen ...

Erweiterte Version vom: 18.8.2012 (Video hinzugefügt) Logarithmen I Definition des Logarithmus. Einführung für Anfänger; Was ist ein Logarithmus