1. Notes Day PAP Algebra 2 Objective: TLW… develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses (2A.11.A) Solve exponential/logarithmic equations using algebraic methods (2A.11.D) use laws of exponents to relate the properties for logarithms Describe limitations on domain and ranges(2A.11.B)

2. Properties of Exponents v Properties of Logarithms
PRODUCT
QUOTIENT
POWER

3. Note we are simplifying not solving for x!
Rewrite each expression as a single logarithm
log818 – log86 1.
log8
y = log b x
log83
Note we are simplifying not solving for x!

4. Note we are simplifying not solving for x!
Rewrite each expression as a single logarithm
log43 + 2log4x + 3log4y 2.
log43 + log4x2 + log4y3
y3 = log b x
log4(3x2y3)
Note we are simplifying not solving for x!

5. Note we are simplifying not solving for x!
Rewrite each expression as a single logarithm 3.
log x + log x – 2 log x
Which btw means 10 0=1 so the simplified answer is 0...but we were asked for a log
log
y3 = log b x
log 1
Note we are simplifying not solving for x!

6. Note we are solving for x !!
Find the value of x in each logarithmic equation 4.
log log325=log3x
log log325 =log3x
y3 = log b x
log3 ( )=log3x
Note we are solving for x !!
log3 (2 5)=log3x
log3 (10)=log3x

7. y3 = log b x SOLVE for x in each logarithmic equation 5.
log33 = log3x – log33
y3 = log b x

8. y3 = log b x SOLVE for x in each logarithmic equation 6.
log427 – (2log46 – log481)=log4x
y3 = log b x

9. Solve for x:
But x = – 6 is not in the reasonable domain

10. Special Logarithm Valuesx x
logabx=_____
xlogab
logaax=___
Change to exp
Change to log
log power rule

11. Find the inverse of each function9.
y = log7x3
x = 3log7y
y = log b x

12. y = log b x 10. 11. Find the inverse of each function y = log(x+1)
y = log(x+1)
y = log(10x)
y = log b x
x = log(10y)
x = log(y+1)
10x =10y
10x = y+1
10x – 1 = y
10(x-1) =y

13. 12. Find the domain and range of
Look above at the parent function of y = log x
Parent
Function
Y=log x X Y
0.1 -1 1 10
10y = x 3
Domain: ________
Range: _________
V. Asymptote: _______ 1
All reals y

14. Activity:
Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer.

15. Solve for x:
A. -36
B. 3
C. 6
D. 28

16. Solve for x:
A. 28
B. 30
C. 60
D. 75

17. Solve for x:
A. 3
B. 4
C. 19
D. 29

18. Solve for x:
A. 1
B. 3
C. 1/3
D. 0

19. Solve for x:
A. 3
B. 6
C. 9
D. 81

20. Solve for x:
A. -36
B. 3
C. 6
D. 28

21. Solve for x:
A. 1
B. 2
C. 9
D. 20

22. Solve for x:
A. 1/5
B. 2
C. 32
D. 10

23. Solve for x:
A. -27
B. -4
C. 9
D. 27

24. Solve for x:
A. 3
B. 5
C. 2/3
D. 30