Introduction to Logarithms Part 1
Dien Algebra 2 Honors
Name:
Period
Graph the following function f ( x ) = 2 x
•
•
Mark 4 “nice” points below and label them in the chart provided.
Graph the line, y = x
x
f ( x) = 2 x
x
f −1 ( x )
What do you remember about inverses?
Use your knowledge about the graphs of inverses and graph the inverse of f ( x ) = 2 x . Label it
f −1 ( x ). Is f −1 ( x ) and exponential graph? _______ What type of graph is f −1 ( x ) ? _______
Now for a deep look into exponential functions:
An exponential Function typically has the form: f ( c ) = b c
•
What happens if the base is 1?
•
What happens if the base is 0?
•
What happens if the base is negative?
Summary:
Introduction to Logarithms Part 1
Dien Algebra 2 Honors
Name:
Period
One way to think of logarithms is as a shortcut for exponents, just like exponents were shortcuts
for multiplication.
Definition:
Exponential Form:
Logarithmic Form:
y = log b ( x ) is read as _______________________________________________________
The variables that appear have special names:
__________________ is the logarithm (the exponent)
__________________ is the base
__________________ is the argument “answer”
Exponential Form
Logarithmic Form
a. 10 = 10, 000
a.
b. 10 −2 = 0.01
b.
c. 2 3 = 8
c.
d. 32 = 9
d.
1
16
1
f. 3−3 =
27
e.
4
e. 2 −4 =
−4
g. 10 =
f.
g.
1
10, 000
Remember Logarithms are exponents!
Base 10 Logarithm:
Base b Logarithm:
Example 1: Rewrite 2 3 = 8 into logarithmic form.
There are three parts of a logarithmic equation that we can solve for….
a.
b.
c.
Introduction to Logarithms Part 1
Dien Algebra 2 Honors
Example 2: Rewrite 2 −3 =
Name:
Period
1
into logarithmic form.
8
Example 3: Rewrite log3 ( x ) = −4 into exponential form and then solve for x.
Example 4: Rewrite log 4 ( 64) = y into exponential form and then solve for y.
Example 5: Rewrite log x ( 4) =
2
into exponential form and then solve for x.
3
Homework, Do this on a separate piece of paper! Do not use a calculator!
For # 1-6, find the argument, x, of the logarithm.
1. log 2 ( x ) = 3
2. log3 x = 3
3. log 1 x = 4
3
4. log 1 x = −4
3
5. log 1 x = 4
6. log 4 x = −
2
1
2
For # 7-12, find the logarithm x.
!1$
"9%
9. log 2 1024 = x
! 1 $
&= x
"
%
5 125
12. log3 (81) = x
7. log 4 16 = x
8. log3 # & = x
10. log 1 243 = x
11. log 1 #
3
For #13-18, find the base, x, of the logarithm.
13. log x 16 = 4
16. log x 81 =
4
3
14. log x 4 = 1
! 1 $ 3
&=
" 216 % 2
17. log x #
!1$
&=2
" 64 %
15. log x #
18. log x 16 = −4