log
2
8
log
2
8 asks the question: “2 to what power is 8?” Based on that, you can answer the following questions:
log
10
1000
=
log
10
1000=
log
10
1,000,000
=
log
10
1,000,000=
Looking at your answers to exercises #3-6, what does the
log
10
log
10
tell you about a number?
Multiple choice: which of the following is closest to
log
10
500
log
10
500 ?
- A. 1
- B.
1
1
2
1
1
2
- C. 2
- D.
2
1
2
2
1
2
- E. 3
log
10
1
10
=
log
10
1
10
=
log
10
1
100
=
log
10
1
100
=
log
2
(0.01)
=
log
2
(0.01)=
log
10
(-1)
=
log
10
(-1)=
log
9
1
81
=
log
9
1
81
=
5log54=
5log54 size 12{5 rSup { size 8{"log" rSub { size 6{5} } 4} } } {}=
OK. When I say
3636 size 12{ sqrt {"36"} } {}
=
6
=6, that’s the same thing as saying
6
2
=
36
6
2
=36. Why? Because
3636 size 12{ sqrt {"36"} } {} asks a question: “What squared equals 36?” So the equation
3636 size 12{ sqrt {"36"} } {}=
6
=6 is providing an answer: “six squared equals 36.”
You can look at logs in a similar way. If I say
log
2
32
=
5
log
2
32=5
I’m asking a question: “2 to what power is 32?” And I’m answering: “two to the fifth power is 32.” So saying
log
2
32
=
5
log
2
32=5 is the same thing as saying
2
5
=
32
2
5
=32.
Based on this kind of reasoning, rewrite the following logarithm statements as exponent statements.
log
3
1
3
=
-1
log
3
1
3
=-1
log
x
(1)
=
0
log
x
(1)=0
Now do the same thing backward: rewrite the following exponent statements as logarithm statements.
8
-
2
3
=
1
4
8-
2
3
=
1
4
Finally...you don’t understand a function until you graph it...
- a. Draw a graph of
y
=
log
2
x
y=
log
2
x . Plot at least 5 points to draw the graph.
- b. What are the domain and range of the graph? What does that tell you about this function?
"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"