WEEK-9.docx

Republic of the Philippines
Department of Education
National Capital Region
Division of Taguig and Pateros
PRES. DIOSDADO MACAPAGAL HIGH SCHOOL
Signal Village National High School- Annex
8th
Street, Barangay Katuparan, GHQ Village, Taguig City
Tel No: 838-56428
TEACHER: MRS. AMIE D. CANDELARIA
QUARTER: 1ST QUARTER (1st
SEMESTER) GRADE LEVEL: GRADE 11 – Ruby M/T 11:30-12:30, WTh 12:30- 1:30; Emerald M/T 12:20-1:30, WTh 1:30-2:30
WEEK: WEEK 9 (OCT 17 - 21, 2022) LEARNING AREA: GENERAL MATHEMATICS
MELC/s: The learner demonstrates understanding of key concepts of logarithmic functions.
DAY OBJECTIVES TOPIC/s CLASSROOM-BASED ACTIVITIES HOME-BASED ACTIVITIES
1
The learner
distinguishes
logarithmic function,
logarithmic
equation, and
logarithmic
inequality.
M11GM-Ih-2
Convert from
exponential to
logarithmic form.
Change from
logarithmic form to
exponential.
Writing Logarithmic
Equations In
Exponential Form
A. Subject Matter: Writing Logarithmic Equations In Exponential Form
a. Reference: General Mathematics Module, GM Book by Orance pp129-134
https://youtu.be/sou4NFobnJE
b. Materials: PowerPoint Presentation, chalk and whiteboard.
c. Value Integration: The art of staying focused and courage to engage in discussion. Time-Consciousness.
B. Routinary Activities
a. Prayer
b. Checking of Attendance/Mental Check
c. Cleanliness and classroom health rules and protocols
d. Checking of Assignment (if any)
C. Review
BMB. Bring Me Back. TRIVIA
LOGARITHM
From the word LOGOS means study or “reckoning” and ARITHMOS means “number “made up by JOHN NAPIER
What sign I am with?
ZIA presentation by group leaders.
D. Motivation
Logarithmic Function, Logarithmic Equation and Logarithmic Inequality
Direction: Identify whether the following as (A) equation, (B) inequality or (C) function.
1. log4 3𝑥 = 5
2. 𝑓(𝑥) = log2 4𝑥 + 1
3. 8 ≤ log2 3𝑥 − 3
4. 𝑦 = log5 2𝑥
5. log7 3𝑥 + log7 2 = 1
6. log6 3𝑥 > 2
I. Assignment:
Take time to watch the link for advanced
study. https://youtu.be/ki3EBVo7UBs

E. Discussion of Concepts
Concept and Properties of Logarithms
INVESTIGATE!
EXPONENTIAL EQUATION LOGARITHMIC EQUATION
22
= 4 log2 4 = 2
34
= 81 log3 81 = 4
91/2
= 3 log9 3 = 1/2
𝑛3
= 64 log𝑛 64 = 3
4𝑛
= 2 log4 2 = 𝑛
𝑎𝑥
= 𝑦 log𝑎 𝑦 = 𝑥
TRY ME!
Rewrite the following logarithmic equations into exponential form.
Change the equations to its logarithmic form.
F. Application
LET”S DIG IN!
Determine whether the given is a logarithmic function, logarithmic equation, logarithmic inequality or neither of the three
options.
G. Generalization
a. What is the relationship of logarithmic to exponential function.
b. Logarithm is denoted by 𝑦 = 𝑙𝑜𝑔a 𝑥 , if and only if 𝑥 = 𝑎𝑦 .
Therefore, logarithm is _____________.
c. Differentiate the logarithmic equation, logarithmic inequality and logarithmic function.
H. Evaluation
Write each logarithmic equation in exponential form.
1. 6 = 𝑙𝑜𝑔2 64
2. 3 = 𝑙𝑜𝑔𝑏 27
3. 𝑙𝑜𝑔3
1
243
= − 527
4. 𝑙𝑜𝑔1
4
1
64
= 3
5. 0.5 = 𝑙𝑜𝑔121 11
Change the equation to its logarithmic form.
1. 34 = 81
2. 6 − 3 =
1
216
log3 81 = 4 log2
1
16
= −4 log𝑎 𝑀 = 7
𝑥 = 𝑙𝑜𝑔𝑐 𝑇 6 = log2 64 log5 𝑥 = 4
72
= 49 𝑒𝑥
= 3 10−2
= 0.01 271/3
= 3 𝑒𝑦
= 9 81= 3
𝑥

3. 122 = 𝑥
4. 8𝑦 = 300
5. 𝑏3 = 343
2
The learner expand and
condense logarithmic
expressions.
M11GM-Ih-2
Basic properties of
logarithm.
Laws of Logarithm.
A. Subject Matter: Properties and Laws of Logarithmic Function
https://youtu.be/ki3EBVo7UBs
b. Materials: PowerPoint Presentation, whiteboard marker and whiteboard
c. Value Integration: Patience The art of staying focused and courage to engage in discussion. Time-Consciousness.
1. Prayer
2. Checking of Attendance/Mental Check
3. Cleanliness and classroom health rules and protocols
4. Checking of Assignment (if any)
C. Review
BMB. Bring Me Back. TRIVIA WITH A TWIST
Basic Properties of Logarithms
1. 𝑙𝑜𝑔𝑏 1 = 0
2. 𝑙𝑜𝑔𝑏 𝑏𝑥 = 𝑥
3. 𝑙𝑜𝑔𝑏 𝑏 = 1
4. 𝑏𝑙𝑜𝑔𝑏 𝑥
= 𝑥, 𝑖𝑓 𝑥 > 0
D. Motivation
EXPLORE.
Use the basic properties of logarithms to find the value of the following logarithmic expression.
1. log 1
2. log 102
= log10 102
3. loge e3
4. log4 64 = log4 43
2. log5
1
125
= log5 5-3
3. log7 7
LAWS OF LOGARITHM
I. Assignment:
Take time to watch the link for advanced
study. https://youtu.be/QfxEudL-srY

Examples:
1. Use the laws of logarithms to expand the expression 𝑙𝑜𝑔 𝑟𝑠3
. Assume each factor is positive.
2. log2 (
4
𝑦
) 5
3. log[𝑥 (𝑥 = 2)]
4. logb u2
√𝑣
5. Use the laws of logarithms to condense each expression to single logarithm log 2 + log 3
6. 2log x + log y
7. 7log3 a -7log3 b
8. 3𝑙𝑜𝑔𝑏 𝑥 + 𝑙𝑜𝑔𝑏(2𝑥 + 1)
F. Application
IT”S YOUR TURN!
Expand.
1. log9 𝑎𝑏
2. log𝑏
𝑥
𝑦2
3
Express as a single logarithm.
3. log𝑎 𝑥 − 𝑙𝑜𝑔𝑎 (2𝑥 + 1)
4. 2𝑙𝑜𝑔 𝑥 + 3𝑙𝑜𝑔 𝑦 + 4𝑙𝑜𝑔 𝑧
G. Generalization
a. Give the four (4) basic properties of logarithm.
b. Discuss the three laws of logarithm.
c.
H. Evaluation
Expand.
1. log5 4𝑛𝑝3
2. log𝑏
4𝑦
𝑥4𝑧
5
3. log𝑏
𝑥2𝑦2
𝑧2
Express as a single logarithm.
4. 7 ln( 𝑥 + 3) −
5. ln 𝑥 5.8 𝑙𝑜𝑔𝑥 + 𝑙𝑜𝑔 𝑦
3
The learner finds the
domain and range of
a logarithmic
function. M11GM-
Ii-3
Domain and Range of
Logarithmic Functions
A. Subject Matter: Domain and Range of Logarithmic Function
a. Reference: General Mathematics Module
https://youtu.be/QfxEudL-srY
b. Materials: PowerPoint Presentation, chalk and whiteboard.
c. Value Integration: The art of staying focused and courage to engage in discussion. Time-Consciousness.
a. Prayer
C. Review
BMB. Bring Me Back.
I. Assignment.
Revisit your learning materials
in preparation of Midterm
Exam.

MENTAL MATH
Discuss the domain and range of exponential function.
D. Motivation
MATH HUGOT
“I DON’T KNOW IF YOU’RE IN MY RANGE, BUT I’D SURE LIKE TO TAKE YOU BACK TO MY DOMAIN”
DOMAIN AND RANGE OF LOGARITHMIC FUNCTION
Definition: The domain of logarithmic function is defined as a set of all positive real numbers while, its range is a set of all
real numbers.
STEPS in determining domain of logarithmic function.
1. Set up an equality showing the argument greater than zero.
2. Solve for x.
3. Write the domain in interval notation.
EXAMPLES:
1. Determine the domain and range of the logarithmic function 𝑦 = 𝑙𝑜𝑔3 (𝑥 − 1) − 3
2. Determine the domain and range of the logarithmic fun1ction 𝑦 = 𝑙𝑜𝑔1
3
(𝑥 + 4).
3. Determine the domain and range of the logarithmic function y = 𝑙og2 (4𝑥 + 16) − 2.
4. Determine the domain and range of the logarithmic function 𝑦 = 𝑙𝑜𝑔 (3𝑥 − 4) − 4.
F. Application
GROUP ACTIVITY! Solve and discuss per group.
Find the domain and range of the following:
𝑓(𝑥) = 𝑙𝑜𝑔2 (𝑥 + 3)
𝑓(𝑥) = log(5 − 2𝑥)
𝑓(𝑥) = log(4𝑥 + 4)
𝑓(𝑥) = 𝑙𝑜𝑔4 (2𝑥 − 3)
𝑦 = 𝑙𝑜𝑔2 𝑥
𝑦 = 𝑙𝑜𝑔2 (𝑥 + 2) − 3
G. Generalization
a. What is the first step in solving domain of 𝑓(𝑥) = 𝑙𝑜𝑔2 (𝑥 + 3)
b. Differentiate the domain and range of exponential and logarithmic function.
c. What is domain and range of logarithmic function?
H. Evaluation
1. Determine the domain of 𝑓(𝑥) = 𝑙𝑜𝑔3 (2𝑥 + 1) − 4
Domain Range
Set Notation {𝑥|𝑥 ∈ ℝ } {𝑦|𝑦 𝜖 ℝ, 𝑦 > 0 }
Interval
Notation
(−∞, +∞) (0, +∞)

2. Find the domain of 𝑓(𝑥) = 𝑙𝑜𝑔 (5 − 2𝑥) − 1
3. Solve for the domain of 𝑓(𝑥) = 𝑙𝑜𝑔1
2
(4𝑥 + 8) + 1
4
The learner determines
the intercepts, zeroes, and
asymptotes of an
logarithmic function.
M11GM-Ii-4
Intercepts, Zeroes and
Asymptotes of an
Exponential Function
A. Subject Matter: Find Intercepts, Zeroes and Asymptotes of Logarithmic Function
b. Materials: PowerPoint Presentation, whiteboard marker and whiteboard
c. Value Integration: Respect, Honesty, Cooperation, Time-Consciousness
a. Prayer
C. Review
BMB. Bring Me Back.
X: “In 2 minutes, find my value”.
1. 2x = -2
2. 2x = 0
3. x - 3 = 5
4. x + 3 = -5
5. -3x = -3
DIXI ROYD ORGANIZER
D. Motivation
ZEROES, INTERCEPT, ASYMPTOTE OF LOGARITHMIC FUNCTION
INTERCEPTS can be x- intercept or y-intercept.
The x- intercept is the abscissa of the point (a, 0) where the graph passes through the x-axis at a. It is the value of x when y = 0.
The y- intercept is the ordinate of the point (0, b) where the graph crosses through the y-axis at b. It is the value of y when x = 0.
When the value of y-intercept does not exist, we write None.
ZEROES are the root or solution of the logarithmic function that is when y = 0.
It is also the x-intercept of the logarithmic function.
ASYMPTOTE of a logarithmic function is always a vertical asymptote, that is x = h in the function 𝒚 = 𝒍𝒐𝒈𝒃 (𝒙 – 𝒉) + 𝒌. It is
the line where the graph approaches but never touches.
ASYMPTOTE OF LOGARITHMIC FUNCTION
I. Assignment
Take time to watch the link for
advanced study.
https://youtu.be/PwxvDVaH06I

Examples:
1. Determine the x-intercept and zeroes of the logarithmic function 𝑦 = 𝑙𝑜𝑔5 (𝑥 – 1).
2. Determine the vertical asymptote of the logarithmic function 𝑦 = 𝑙𝑜𝑔5 (𝑥 – 1).
3. Determine the x-intercept, zero and vertical asymptote of the logarithmic function 𝑦 = 𝑙𝑜𝑔2 (𝑥 + 3).
4. Determine the x-intercept, zero and vertical asymptote of the logarithmic function 𝑦 = 3𝑙𝑜𝑔2 (𝑥).
5. Determine the x-intercept, zero and vertical asymptote of the logarithmic function 𝑦 = 𝑙𝑜𝑔3 (𝑥 − 2).
F. Application
LET’S DIG IN!
Find the zeroes, intercept of the following.
𝑦 = 𝑙𝑜𝑔2 (𝑥 + 2)– 3
𝑦 =log2 𝑥
𝑓(𝑥) = 𝑙𝑜𝑔2 (𝑥 + 4) − 1
Find the asymptote of the following.
𝑓(𝑥) = 𝑙𝑜𝑔 (3𝑥 − 2)
𝑓(𝑥) = log(𝑥 + 3) + 2
𝑓(𝑥) = 𝑙𝑜𝑔1
2
(2𝑥 − 5) − 4
G. Generalization
a. What is an asymptote of logarithmic function?
b. Describe the zeros and x-intercept of logarithmic function.
c. Describe the graph of logarithmic function.
H. Evaluation
LET:S APPLY!
Question 1. A graph gets closer and closer as the x r y increases or decreases its value without bound.
Question 2: The root or solution of the logarithmic function that is when y = 0.
Question 3: (True or False) Set the value of y = 0 to solve x.
PREPARED BY: CHECKED BY: RECORDED BY:
MRS. AMIE D. CANDELARIA MRS. BRIGITTE G. GAGARIN MRS. NARIZA JANE B. TAMUNDONG
General Mathematics Teacher Mathematics Department Coordinator Academic School Head

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