6.2: Logarithms

A logarithm of a number is the value of the exponent to which the base must be raised to produce a given number. For example: log3(81)=4 because 3^4=81.





A logarithm is the inverse of a function, where the x and y values are switched. Therefore if y=b^x, the inverse of this function is x=b^y which is represented by y= logb(x). y equals the logarithm of x to the base b. The logarithmic function is useful for solving unknown exponents.

The graph displays the exponential function y= 2^x, along with its inverse, y= log2(x). They reflect on the y=x axis.

To write an exponential equation in logarithmic form we...

16 = 2^4

4 = log2 (16)

We read this by saying "4 equals the logarithm of 16 to the base 2".

To write a logarithmic equation in exponential form we ...

log3 (81)

let y = log3 (81)

Then, 3^y = 81

3^y = 3^4

y= 4

NOTE: common logarithms are logarithms with a base of 10. Many times questions will not state the base of 10 because it is understood that the base is 10.

This video will help you further understand logarithms... it sure helped me!