Unit 5 Lesson 6
Algebra 2 CP – U5L6: Introduction to Logarithms
1. Do Now: See Board
2. Objective: ________________________________________________________________________________
3. Guided practice:
Algebraic
Numerical
Directions: Today we will learn about the inverse of You completed a table of values for f (x) as a Do
an exponential function such as
Now. Now use what we learned about inverses in
unit 4 to complete a table for f 1 ( x) .
f ( x)  2 x
The inverse of an exponential function is called a
logarithm. We will be learning about these today.
f 1 ( x)  log 2 x
x
-2 -1
0
1
2
f (x )
x
f
1
1
4
1
2
1
2
4
( x)
Graphical
Communication
Directions: f(x) is given below. Sketch your function
f-1(x) from above.
1. Explain what you notice about graph of f(x)
compared to the graph of the inverse function
f 1 ( x) .
y









x
























2. Find the domain and range of f(x) and the
inverse using the graph.
f (x )
---------f 1 ( x)
Domain
Range
3. What do you notice about the domain and range
of each function?





4. Find the x- and y- intercepts of each function.
f (x )
---------f 1 ( x)
x – intercept
y – intercept
5. What do you notice about the x- and y- of
intercepts of each function?
4. Introduction to Logarithms
The inverse relationship that we saw in the previous example leads to concept called
a logarithm.
Logarithms:
𝒃𝒙 = 𝒚 → 𝒍𝒐𝒈𝒃 𝒚 = 𝒙
In other words, if a number b is raised to the x power, and you get the answer y, then
the logarithm base b of the answer y is the exponent x.
Now, let’s use the answers from the numerical box on the prior page to for some
examples.
Exponential
1
If 2−2 = then….
Logarithm
1
= −2
4
1
𝑙𝑜𝑔2 =
2
𝑙𝑜𝑔2
4
1
If 2−1 = then…
2
If 20 = 1 then…
𝑙𝑜𝑔2 1 =
If 21 = 2 then…
𝑙𝑜𝑔2 2 =
If 22 = 4 then…
𝑙𝑜𝑔2 4 =
5. Group practice: Evaluating Logarithmic Expressions Using a Log Table
Example
1.
log3 81
2.
log6 1296
3.
log9 729
Exponential
Expression
Logarithmic
Expression
Comments,
Questions,
Reminders
Group practice (cont.)
Example
Exponential
Expression
Exact Value
Comments,
Questions,
Reminders
1.
log 5
1
25
2.
log 1 8
2
3.
log9 3
Logarithmic
Expression
1.
log7 343
2.
log 4 16
3.
log5 125
4.
log2 256
5.
log8 4096
6.
log9 9
7.
log8 1
Exponential Expression
Exact Value
6. Change of base formula and calculator usage.
The Change of Base Formula:
𝑙𝑜𝑔𝑏 𝑦 =
𝑙𝑜𝑔𝑐 𝑦
𝑙𝑜𝑔𝑐 𝑏
This formula can be especially useful for evaluating a logarithm in a calculator,
since the only bases available in most calculators are 10 and “e” (this is called the
natural logarithm).
Use your calculator to evaluate these logarithms:
Logarithmic
Expression
1.
1
log 5
5
2.
log36
1
6
3.
log105 11, 025
4.
log4 4-0.38
Exponential Expression
Exact Value