1. FAC2bD2-3 Have out: Bellwork:
Assignment, pencil, red pen, highlighter, notebook, calculator
FAC2bD2-3
Have out:
Bellwork:
Solve for x. 1) 2) 3) +1 +1 +1 +1 +1 +1
x = 3 +2
x = 5 +1 +2
x – 7 = 0 or
x +5 = 0
x = 7 +1
x = –5 +1
Check!!!
total:
x = 7 +1

2. The Rules of Exponents:
Review
Rule:
Example:
Keyword:
23+5
=28
Product 1)
bx+y
bx–y
38–5
= 33
Quotient 2)
bxy
42(3)
= 46
Power 3)

3. Name parts of a logarithm
Argument
Base
Exponent

4. Complete the calculations for Part 1a on your calculator.
Be sure to locate the LOG function on your calculator.
LOG button
Note: the LOG function on your calculator is base 10, that is:
log( ) means log10( )

5. 1 x • y + The __________ Property of Logarithms
multiply
log 5 = _________
log 6 = _________
log 30 = _________
log 7 = ________
log 2 = ________
log 14 = ________
log 12 = _________
log 3 = _________
log 36 = _________
When you ________ the arguments, you ______ the exponents.
0.70
0.85
add
0.78
0.30
1.48
1.15
1.08
multiply
0.48
add
1.56
The __________ Property of Logarithms
log x + log y = log (________)
Conversely: log (x ∙ y) = log (x) ____ log (y)
Product
x • y +

6. 1c) Practice: Use the property to rewrite each expression as a single logarithm.
ii)
iii)
1d) Practice: Express in expanded form. i)
ii)
iii)

7. The __________ Property of Logarithms2
divide
1.90
1.75
log 80 = _________
log 8 = __________
log 10 = _________
log 56 = _________
log 8 = _________
log 7 = __________
log 36 = _________
log 4 = __________
log 9 = __________
When you _______ the arguments, you ________ the exponents.
subtract
0.90
0.90
1.0
0.85
1.56
divide
0.60
subtract
0.95
The __________ Property of Logarithms
log x – log y = log ( )
Conversely: log = log (x) ____ log (y)
Quotient
x y –

8. 2c) Practice: Use the property to rewrite each expression as a single logarithm.
ii)
iii)
2d) Practice: Express in expanded form. i)
ii)
iii)

9. The ______ Property of Logarithms Conversely: b log a = log (____)3
Use the product rule!
log (52) = log ( ________)
= log (____) + log (____)
= __________________
log (82) = log ( ________)
= log (__) + log (__)
= ______________
Write log 63 as the sum of three logs, then simplify:
log (63) = log ( ________)
= log (__) + log (__) + log (__)
Let’s use a calculator:
Find: log (34) =________
Find: 4 log 3 = _______
5 ∙ 5
8 ∙ 8 5 5 8 8
2 log 5
2 log 8
1.91
6 ∙ 6 ∙ 6
1.91 6 6 6
3 log 6
The ______ Property of Logarithms
log (ab) = (___)log a
Conversely: b log a = log (____)
Power b ab

10. 3c) Practice: Use the property to rewrite each expression.
ii)
iii)
3d) Practice: Rewrite without the coefficients, then simplify. i)
ii)
iii)

11. MIXED PRACTICE
1. Rewrite each expression as a single logarithm. Simplify, if possible.
a) log 5 + log 7
b) log 15 – log 5
c) log 9 – log 3
log (5 • 7)
log 35
log 3
log 3 d) e) f)

12. MIXED PRACTICE
1. Rewrite each expression as a single logarithm. Simplify, if possible. g) h) i) j) k) l)

13. 2. Express in expanded form.b) c) d) e) f)

14. a) 3. Solve the equations. Check your solutions.
To solve problems such as this, we need to use the product property to put the logs on the left side together.
Now the problem is written:
log ( ) = log ( )
Use the property of equality to set the arguments equal, then solve.
We are going to work on the problems in the first column.
Skip to part (c) now.

15. c) 3. Solve the equations. Check your solutions.
Use the quotient property to combine the left side.
Now the problem is written:
log ( ) = log ( )
Use the property of equality to set the arguments equal, then solve.

16. e) 3. Solve the equations. Check your solutions.
Use the power property to move the coefficient. e)
Use the quotient property to combine the right side.
Now the problem is written:
log ( ) = log ( )
Use the property of equality to set the arguments equal, then solve.

17. g) 3. Solve the equations. Check your solutions.
Use the power property to move the coefficient. g)
Use the product property to combine the right side.
Now the problem is written:
log ( ) = log ( )
Use the property of equality to set the arguments equal, then solve.

18. Finish today's assignment:
Worksheet