lesson 3.2 read: pages 207-209 3.2 handout 1-49 (odd), 55, 59, 63, 68, 69-75 (odd)
TRANSCRIPT
Lesson 3.2
Read: Pages 207-209
3.2 Handout1-49 (ODD), 55, 59, 63, 68, 69-75 (ODD)
Logarithmic Function and Their Graphs
Objective
Students will know how to recognize, graph, and evaluate logarithmic functions.
y loga x
Common Logarithm - a logarithm with base 10.
log10 or log
Natural Logarithm - a logarithm with base e.
loge or ln
Write each of the following equations in exponential form.
log5 1 0
log3
1
9
2
logx 2 3
ln x 2
Write each of the following equations in logarithmic form.
53 125
25
3
2 1
125
100.5 10
e 5 y
e5x y 6
Simplify each of the following expressions.
log3 81
log8 8
log 10
log27 3
log5 0.2
log9 1
log7 76
Simplify each of the following expressions.
ln e5
ln1
e
ln e2x
Simplify each of the following expressions.
10log 4
e ln 2
e ln x
Find the value of x in each of the following equations. Write all answers in simplest form.
log5 125 x
logx 36 2
log32 x 1
5
log16 32 x
ln x 5
ln x 2 3
Solve for x. Give an exact answer, and then use a calculator to round that answer to the nearest thousandth.
10x 45
ex 4
7
e5x1 7
10x2 1 7
Graphs of Logarithmic Functions
Step 1:
Step 2: Use your value of h (horizontal shift) to relocate your vertical asymptote.
Use your transformations to relocate the point (1,0).
Step 3: Plot a point to the right and left of the relocated point (1,0).
Step 4: Sketch your graph.
𝑓 (𝑥 )=𝑎 log𝑏 (𝑥−h )+𝑘
(a) Use transformations to sketch the graph of the function. Clearly label any asymptotes. (b) State the domain and range of the function. (c) State whether the graph is increasing or decreasing.
f x log6(x 4) 2
f x ln x 4
f x log x 1
Algebraically find the domain of each of the following functions.
f x log5 x
f x log x 3
f x log3 3 4x 5