Post on 03-Jan-2016
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4.4 – Evaluate Logarithms and Graph Logarithmic
FunctionsGPS: MM3A2c, MM3A2e, MM3A2f
GPS MM3A2c – Define logarithmic functions as
inverses of exponential functions. MM3A2f – Graph functions as transformations
of f(x) = ax, f(x) = logax, f(x) = ex, f(x) = ln x. MM3A2e – Investigate and explain
characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.
Let b and y be positive numbers with b≠ 1. The logarithm of y with base b is denoted by and is defined as follows: = x if and only if
A common logarithm is a logarithm with base 10, denoted by log.
A natural logarithm is a logarithm with base e, denoted by ln.
A logarithmic function is a function of the form .
By definition of a logarithm, it follows that the logarithmic function is the inverse of the exponential function .
Vocabulary
Logarithmic Form Exponential Form
Example 1: Rewrite logarithmic equations (Page 145)
Evaluate the logarithm.
Example 2: Evaluate logarithms
b.) c) d)
Try page 145, 1-8
Guided Practice
What are these?
Before we answer that, what is a function? ◦ Think maps◦ How would we solve the following functions?
What are Inverses?
Domain Range
2
3
1) Switch the x and y2) Solve for y 3) How do we get rid of
different things like logs or natural logs?
4) Denote by using thefollowing:
Steps to finding the inverse of a function
• Logs are “undone” by exponents – and vice versa
• Natural logs (ln) are undone by e – or vice versa
Example
Find the inverse of the function.a) From the definition of logarithm, the
inverse of is
Find inverse function (Page 146)
Original function
Switch x and y
Write in exponential form.
Solve for y.
*The inverse is when you solve for y*
Graph State the domain and range.Same rules apply
Translate a logarithmic graph