Logarithmic Functions:
Intro & Graphing
TS: Making decisions after reflection and review
Warm-Up
1) log416 = 2 is the logarithmic form of 4░ = 16
2) 34 = 81 is the exponential form of log ░ ░ = 4
3) log464 =
4) log2 ¼ =
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)
1) loga1 = 0 because a0 = 1
2) logaa = 1 because a1 = a
3) logaax = x and alogax = x. (Inverse Property)
4) If logax = logay, then x = y. (One-to-One Property)
Using the Definition to Convert
between forms
Write each in
exponential form
Write each in
logarithmic form
1) log3y = -4
1) 2x = 15
2) ln b = a
2) e3 = y
3) log 15 = x
3) 103 = 1000
Evaluate or Solve each logarithmic
expression or equation
1) log71/49
Solve for x:
2) log168
1) log2x = log28
3) log0.001
4) log√28
2) log4x = -2
*5) log345
*6) ln 5
3) 3log3x = 7
Logarithmic Functions are inverses
of _______________
Given the above
graph of y = 4x,
graph y = log4x
Given the above
graph of y = ex,
graph y = ln x
Given the above graph
of y = log3x, graph
y = log3(x+2) – 3
What is the domain
& range of y = log4x
What is the domain
& range of y = ln x
What is the domain &
range of y = log3(x+2)–3
Graphing Using Translations
Give the domain and range & graph each.
1) f(x) = log4(x – 2) + 3
Graphing Using Translations
Give the domain and range & graph each.
2) y = -logx – 3
Graphing Using Translations
Give the domain and range & graph each.
3) y = 3 + log2(-x + 1)
Graphing Using Translations
Give the domain and range & graph each.
4) y = ln(2 – x)
Graphing Using Translations
5)Given the function is a translated
form of y=log3x, find
the equation of the graph.