1. Logarithmic Functions (Day 1)
Algebra 2: Section 8.4
Logarithmic Functions (Day 1)

2. Solving for “x” Addition x – 3 = 5 Subtraction 3 + x = 9
Multiplication 1/2x = 4
Division 5x = 25
Power x3 = 27
Roots
If “x” is an exponent?

3. Definition of Logarithm
logby is read as “log base b of y”

4. Rewrite the equations in exponential form.
Examples
Rewrite the equations in exponential form.
Logarithmic Function
Exponential Function
1. log39 = 2
2. log81 = 0
3. log5 (1/25) = -2
1. 32 = 9
2. 80 = 1
= 1/25

5. Examples
Evaluate the expressions. Hint: For logby ask yourself what power of b gives you y?
4. log464
What power of 4 gives you 64?
4x = 64
Answer: 3
5. log20.125
What power of 2 gives you 0.125?
2x = 0.125
Answer: -3
6. log1/4256
What power of ¼ gives you 256?
1/4x = 256
Answer: -4
7. log322
What power of 32 gives you 2?
32x = 2
Answer: 1/5

6. Common and Natural Logs
Common Logarithm
(the base of 10 is not written)
log10x = log x
Natural Logarithm
(remember “e” = natural base)
logex = ln x

7. Examples Evaluate: (Round to 3 decimals) 8. log 7 9. ln 0.25 = -1.386
= 0.845
9. ln 0.25 =
On TI-83:
LOG button is base 10 and is to the left of 7
LN button is base e and is to the left of 4

8. Logarithm Inverse Properties

9. Examples
Simplify the expressions.

10. Finding Inverses of Logarithms
SAME Steps as Before!!!
First, switch the x’s and y’s.
Rewrite the logarithm equation as an exponential equation.
Solve for y.

11. Examples x = log8y 8x = y y = 8x
Find the inverse of the following functions.
14. y = log8 x
x = log8y
8x = y
y = 8x

12. Examples
15. y = ln (x – 10)
x = ln(y – 10)
ex = y – 10
y = ex + 10

14. Homework
p.490 #16-64 evens

15. Logarithmic Functions (Day 2) (Graphing…yeah!)
Algebra 2: Section 8.4
Logarithmic Functions (Day 2) (Graphing…yeah!)

16. Definition of Logarithm (Reminder)

17. Change of Base Formula
Used to evaluate logs that are bases other than 10 or e.
Or to punch logs of base other than 10 or e into the calculator (for graphing).

18. Graphs of Logarithmic Functions

19. Graphs of Logarithmic Functions
y = logb(x – h) + k
Asymptote: h (x = “h”)
Domain: Range:
If b>1, curve opens up
If 0<b<1, curve opens down
To graph:
Show the asymptote
Plot the x-intercept (calc or…..)
find by setting y = 0 (will have to do for SEVERAL!!!)
rewrite as an exponential equation
Solve for x

20. How to write in Calculator

21. Examples
State the asymptote, the domain, and the range of each function.
1. y = log1/2x + 4

22. Examples
2. y = log3(x – 2)

23. Homework p.491 #65-76 all State asymptote, x-intercept, domain, range
Be sure asymptotes are graphed and labeled