1. 1) log416 = 2 is the logarithmic form of 4░ = 16
Logarithmic Functions: Intro & Graphing TS: Making decisions after reflection and review
Warm-Up
1) log416 = 2 is the logarithmic form of 4░ = 16
34 = 81 is the exponential form of log ░ ░ = 4
log464 =
log2 ¼ =

2. Definition of a Logarithmic Function (p.274)
For x > 0, a > 0 and a ≠ 1,
y = logax if and only if x = ay
Where f(x) = logax is called the logarithmic function with base a.
Properties of Logarithms (p. 274)
loga1 = 0 because a0 = 1
logaa = 1 because a1 = a
logaax = x and alogax = x. (Inverse Property)
If logax = logay, then x = y. (One-to-One Property)

3. Using the Definition to Convert between forms
Write each in Write each in
exponential form logarithmic form
log3y = ) 2x = 15
ln b = a 2) e3 = y
log 15 = x 3) 103 = 1000

4. Evaluate or Solve each logarithmic expression or equation
1) log71/49 Solve for x:
2) log ) log2x = log28
3) log0.001
4) log√ ) log4x = -2
*5) log345
*6) ln ) 3log3x = 7

5. Logarithmic Functions are inverses of _______________
Given the above graph of y = 4x, graph y = log4x
What is the domain & range of y = log4x
Given the above graph of y = ex, graph y = ln x
What is the domain & range of y = ln x
Given the above graph of y = log3x, graph y = log3(x+2) – 3
What is the domain & range of y = log3(x+2)–3

6. Graphing Using Translations
Give the domain and range & graph each.
f(x) = log4(x – 2) + 3

7. Graphing Using Translations
Give the domain and range & graph each.
2) y = -logx – 3

8. Graphing Using Translations
Give the domain and range & graph each.
3) y = 3 + log2(-x + 1)

9. Graphing Using Translations
Give the domain and range & graph each.
4) y = ln(2 – x)

10. Graphing Using Translations
5)Given the function is a translated
form of y=log3x, find
the equation of the graph.