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.

# Logarithms

The function f(x) = 2x is called an exponential function because the variable, x, is the exponent. In general, exponential functions are of the form f(x) = ax, where a is a positive constant. The inverse of an exponential function is called a logarithmic function. Therefore, the inverse of f(x) = ax is the logarithmic function with base a, such that y = logax ↔ ay = x. In many science applications, we are interested in base 10 logarithms.

## Evaluating Logarithms

In science it is important to be able to evaluate log functions, as they come up in many applications. To evaluate the log (base 10) of a number, type the number into your calculator then hit the [log] key. Some calculators are slightly different; therefore, it is important for students to be familiar with their own calculator. It is also important in many situations to be able to determine the antilog of a log value. To evaluate the antilog of a number, type the number into the calculator and hit the [10x] key.

Example: Find x in each of the following equations: x = log103.6 and log10x = 6.75.

Solution:

x = log103.6                                         log10x = 6.75.

x = 0.556                                                      x= 5.62x106

Example: Convert [H+] = 3.5x10-3 M to pH.

Solution:

pH = -log[H+]

pH = -log [3.5 x 10-3]

pH = 2.4

Example: What value of [H+corresponds to a pH of 4.3?

Solution:

pH = -log [H+]

4.3 = -log [H+]

-4.3  = log [H+]

[H+] = 10-4.3

[H+] = 5.0 x 10-5﻿ M

Example: