# Semi-Log and Log-Log Graphs

Let's take a closer look at the difference between semi-log and log-log graphs.

## Plotting on Logarithmic Paper

Logs are helpful when plotting certain types of data. There are two types of log graphs that can be used when plotting data.

### Semi-log Graph

The first is called a semi-log graph. In a semi-log graph the y-axis is logarithmic, which means the seperation between the ticks on the graph is proportional to the logarithm of numbers. The x-axis has a linear scale, which means the ticks are evenly spaced.

A semi-log graph is useful when graphing exponential functions. Consider a function of the form y = ba^{x}. When graphed on semi-log paper, this function will produce a straight line with slope **log (a)** and y-intercept **b**.

**Example:** Plot the function y = 5^{x} on an ordinary axis (x- and y- linear scales) as well as on a semi-log axis.

*Solution:* Both functions below:

## Log-log Graph

The second type is called a log-log graph. In a log-log graph, both the x-axis and the y-axis are logarithmic.

This is useful for determining power relationships. If a function of the form y = ax^{n} is graphed on log-log paper, a straight line will be produced, with slope **n** and y-intercept **log (a)**.

**Semi-Log Graph Example:**

**Log-Log Graph Example:**