[PDF] 4 Logarithmes

What is a common logarithm?

This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number. Another base that is often used is e (Euler's Number) which is about 2.71828. This is called a "natural logarithm".

How do you write a logarithm?

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8. In the same fashion, since 10 2 = 100, then 2 = log 10 100.

What is the base of a logarithm?

While the base of a logarithm can have many different values, there are two bases that are used more often than others. Specifically, most calculators have buttons for only these two types of logarithms. Let's check them out. The common logarithm is a logarithm whose base is 10 10 ("base- 10 10 logarithm").

What is the logarithm of a product?

The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two numbers is the difference of the logarithms. The logarithm of the p -th power of a number is p times the logarithm of the number itself; the logarithm of a p -th root is the logarithm of the number divided by p.