6.2 Logarithms

The concept of logarithms was created by John Napier, in order to simplify math, specifically for the use of astronomers. Previously, the only way to solve exponential equations, such as 25=10^x, was using the "guess & check" method. Now, logarithms can be used to solve such equations much more easily and provide an exact answer.

A logarithm of a function is the inverse of the function. Essentially, the input and output of the equation have switched roles.

For the equation: y=b^x, the inverse is: x=b^y, which is represented as y=logbx. This means that y is equal to the log base b of x.

The above graph displays the relationship between a function and the logarithm of that function. The two functions are reflections of each other about the y=x graph.

The following are examples of the relationship between the exponential and logarithmic forms of equations:

Logarithms to the base of 10 are known as common logarithms. Most of the logarithms we will encounter in this chapter are common ones, and these are the only logarithms that we can currently solve using calculators. When writing a common logarithm, it is not necessary to write the base number (10).

For example:

log27 = log₁₀27

The following are examples of common logarithms:

***Hint: need to understand/apply this for the thinking/inquiry section on quiz***