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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

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.

Semi-log graph

A semi-log graph is useful when graphing exponential functions. Consider a function of the form y = bax. 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 = 5x on an ordinary axis (x- and y- linear scales) as well as on a semi-log axis. 

Solution: Both functions below:

Ordinary axis versus semi-log axis

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.

Log-log Graph

This is useful for determining power relationships. If a function of the form y = axn 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: