#### So what does a log graph look like?

There are two main 'shapes' that a logarithmic graph takes. Depending on whether * b* in the equation $$ y= log_b (x) $$ is less than 1 or greater than 1.

**Note:** The two pictures up above do not include the case of b =1

Can you figure out why? What is special about the graph of $$ y = log_1 (x) $$?

Property 6

Grow very slowly for large X (see application below)

Property 7

Do have horizontal asymptotes?

**Not**

**Remember: **Inverse functions have 'swapped' x,y pairs.

**Practice** Problems

Logarithmic graphs

#### What are some applications of Logarithmic Graphs?

There are many real world examples of logarithmic relationships. Logarithms graphs are well suited

- when you are interested in
*quantifying relative*change instead of*absolute difference*. Consider for instance the graph #1 below. - when you want to
*compress large scale data*. Consider for instance that the scale of the graph below ranges from 1,000 to 100,000 on the y-axis and 1 to 100 on the x-axis--such large scales which can be typical in scientific data are often more easily represented logarithmically. - pH scale for measuring acidity of a substance, decibel levels for audio measurement and the Richter scale for measuring earthquakes are all logarithmic. Read more at wikipedia about this