Logarithmic Functions Lesson

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In this section, we will learn about logarithmic functions. In a previous lesson, we learned about exponential functions such as: f(x) =
a^{x}. When we take the inverse of this function, we end up with: x = a^{y}. Up to this point, we have not learned any method
that would allow us to solve for the dependent variable y. Logarithms provide a way to perform this operation. We can say that: y = log_{a}(x)
is the same as: x = a^{y}. So for all intents and purposes, a logarithm is an exponent. When we see log_{a} (x), we are asking for the exponent to
which the base (a) must be raised to obtain (x). As an example, suppose we see: log_{2} (8). We are asking what exponent must the base (2) be
raised to, in order to obtain 8. The answer is 3, since 2^{3} = 8 : log_{2} (8) = 3. We will begin by learning how to convert between exponential
and logarithmic form. The process is fairly simple, we just need to understand what is being isolated in each scenario. In exponential form: 3^{2} = 9,
here 9, the power is isolated. In logarithmic form, we have: log_{3} (9) = 2, here 2, the exponent is isolated. We will then move into solving
logarithmic equations. We solve these equations by converting into exponential form and solving the resulting equation. Lastly, we will look at how to
sketch the graph of a logarithmic function.

Logarithmic Functions Resources:

Videos:

Khan Academy - Video
Khan Academy - Video
Think Well - YouTube - Video
Text Lessons:

Khan Academy - Text Lesson
Cliffs Notes - Text Lesson
WTAMU EDU - Text Lesson
Worksheets:

Math-Aids - Worksheet
Kuta - Worksheet
Khan Academy - Practice
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