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Logarithms

Why Use Logarithms?

Suppose we have a very efficient way of writing any number as powers of a fixed number, say 10:

x = 10m

y = 10n

Then we can perform multiplication and division by using addition and subtraction (of exponents):

xy = 10m+n

x/y=10^(m-n) = 10m−n

A logarithm is just another name for an exponent with respect to a certain base such as 10.

 

The General Logarithm

Let b > 0.

If  y = bx,    then we write logb(y) = x or simply  logb y = x    (read "log of y with base b")

Note:   logb y is not defined for y ≤ 0 , as y = bx > 0 for any x (as b > 0).

Example

32 = 2^5 if and only if log base 2 of 32 equals 5

More Examples

Exercise

For this exercise, evaluate the logarithm, to the base shown, of the number.

log   =
   

 

Logarithms Index | Rules >>

 

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