Demo: Properties of Logarithms - Part 2

Duration: 21 min

This video lesson is available to enrolled students.

Return to /learn/DSSSB-TGT-COMPUTER-SCIENCE-COMPLETE-COURSE/arithmetical-numerical-ability/logarithm/laws-or-properties-or-rules-of-logarithms/asset-demo-properties-of-logarithms-part-2 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness / सामान्य जागरूकता: Polity / राजव्यवस्था, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Biology / जीव विज्ञान, Chemistry / रसायन विज्ञान, Static General Knowledge / स्थैतिक सामान्य ज्ञान, History / इतिहास, Geography / भूगोल, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Evolution of Indian Banking (Banking & Financial Awareness), Environment / पर्यावरण
  3. Section A: General Intelligence & Reasoning ability / सामान्य बुद्धिमत्ता एवं तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Data Sufficiency / आँकड़ों की पर्याप्तता, Non-Verbal Reasoning / अशाब्दिक तर्क, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Blood Relations / रक्त संबंध, Syllogisms / न्यायवाक्य, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Direction and Distance / दिशा एवं दूरी, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Data Sufficiency and Decision Making / आँकड़ों की पर्याप्तता एवं निर्णय क्षमता, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Crypt Arithmetic / कूट अंकगणित, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Data Arrangement / आँकड़ों की व्यवस्था, Inequality / असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, TCS NQT Advanced Reasoning Ability / TCS NQT उन्नत तर्कशक्ति क्षमता
  4. Section A: Arithmetical & Numerical Ability / अंकगणितीय एवं संख्यात्मक योग्यता: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Data Interpretation / आँकड़ा निर्वचन, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Logarithm / लघुगणक, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Time, Speed and Distance / समय, चाल और दूरी, Percentage / प्रतिशत, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time and Work / समय और कार्य, Pipe and Cistern / नल और टंकी, Solid Mensuration / घन क्षेत्रमिति, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Algebra / बीजगणित, Probability / प्रायिकता, Mental Ability / मानसिक योग्यता, Age Problems / आयु संबंधी प्रश्न, Partnership / साझेदारी, Statistics / सांख्यिकी, Arithmetic / अंकगणित, Speed Mathematics and Basic Mathematics / द्रुत गणित और आधारभूत गणित, Miscellaneous / विविध
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Reading Comprehension, Parts of Speech, Sentence Construction, Prepositions and Conjunctions, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Structure and Common Errors, Modals, Transformation of Sentences, Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: हिंदी भाषा एवं बोध / Hindi Language & Comprehension: भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, बहुविषयक सामग्री (विभिन्न अवधारणाओं से संबंधित सामग्री), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology / शिक्षण पद्धति: Growth and Development / वृद्धि और विकास, Concept of Pedagogy / शिक्षाशास्त्र की संकल्पना, Theories of Development / विकास के सिद्धांत, Inclusive Education / समावेशी शिक्षा, Experiential Pedagogy / अनुभवात्मक शिक्षाशास्त्र, Assessment and Evaluation / आकलन और मूल्यांकन, Socialisation and Gender / समाजीकरण और जेंडर, National Education Policy (NEP) 2020 / राष्ट्रीय शिक्षा नीति (NEP) 2020, Cognitive Processes / संज्ञानात्मक प्रक्रियाएँ, Teaching Planning and Teaching Skills / शिक्षण योजना और शिक्षण कौशल, Personality Development / व्यक्तित्व विकास, Teaching Methods / शिक्षण विधियाँ, Learning and Behavioural Theories / अधिगम और व्यवहारवादी सिद्धांत, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Assessment and Evaluation / आकलन एवं मूल्यांकन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, Computer Fundamentals, Cyber Safety and Security, Computer Software, Operating System, Word Processing (MS Word), Computer Networks, Presentation Software (MS PowerPoint)
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics / गणित: Linear Algebra / रैखिक बीजगणित, Calculus / कलन, Trigonometry / त्रिकोणमिति, Vectors / सदिश, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps / शोध प्रक्रिया के चरण, Graph Theory, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Euclidean Geometry and Mensuration / यूक्लिडीय ज्यामिति और क्षेत्रमिति, Statistics and Probability / सांख्यिकी और प्रायिकता, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ, Plane Mensuration / समतल क्षेत्रमिति, Sampling / प्रतिचयन
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management / व्यवसाय अध्ययन एवं प्रबंधन: Business Communication / व्यावसायिक संचार, Principles and Functions of Management / प्रबंध के सिद्धांत एवं कार्य, Accounting Fundamentals and Recording of Transactions / लेखांकन के आधार एवं लेन-देनों का अभिलेखन, Business Economics / व्यावसायिक अर्थशास्त्र, Depreciation, Final Accounts and Computerised Accounting / ह्रास, अंतिम खाते व कंप्यूटरीकृत लेखांकन, Knowledge Management & New Economy / ज्ञान प्रबंधन और नई अर्थव्यवस्था
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a detailed exploration of advanced logarithmic properties, specifically focusing on the Power Rule, Double Power Rule, Base Changing Rule, and a unique Active Passive Voice identity. The instructor systematically introduces each property with formal definitions, algebraic proofs, and practical applications. Key concepts include the Power Rule (Property 5), which states that log_a(x^n) equals n times log_a(x). The lesson progresses to the Double Power Rule (Property 6), handling cases where both the base and argument have exponents, resulting in a coefficient of n/p. The Base Changing Rule (Property 7) is introduced to facilitate conversion between different logarithmic bases. Finally, the video concludes with Property 8, an identity relating a^log b and b^log a through an analogy of active and passive voice. The teaching method relies heavily on whiteboard demonstrations, step-by-step algebraic derivations, and specific numerical examples to reinforce understanding.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins by introducing Property 5, the Power Rule for logarithms. The instructor displays the formula log_a(x^n) = n * log_a(x) on screen, explicitly noting the conditions x > 0, a > 0, and a ≠ 1. Visual cues include underlining the base 'a' and circling the exponent 'n' inside the logarithm to emphasize its movement. The instructor writes log_a(x^n) on the whiteboard, demonstrating how to rewrite expressions with exponents inside the logarithm by bringing the exponent out as a multiplier. This section establishes the foundational rule for manipulating powers within logarithmic arguments.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to prove Property 5 using algebraic substitution. By setting log_a(x^n) = k, the expression is converted to exponential form x^n = a^k. Solving for x yields x = a^(k/n), which is then substituted back to show that k/n equals log_a(x). This derivation confirms the relationship. The lesson transitions into a practical application with the problem: Find the value of log_10(100)^2. The instructor sets y equal to this expression and applies the power rule, rewriting it as 2 * log_10(100). The step-by-step simplification continues, showing 2 * log_10(10^2), which becomes 2 * 2 * log_10(10). This segment bridges theoretical proof with numerical calculation.

  3. 5:00 – 10:00 05:00-10:00

    The video introduces Property 6, the Double Power Rule, which generalizes the handling of exponents in both the base and the argument. The formula log_a^p(m^n) = n/p * log_a(m) is displayed, indicating that the input power 'n' moves to the front as a multiplier while the base power 'p' becomes its reciprocal in the denominator. The instructor breaks down the logic: input powers move as is, while base powers become reciprocals. The lesson then transitions to Property 7, the Base Changing Rule, showing the formula log_b(a) = log_x(a) / log_x(b). This rule allows conversion of a logarithm from one base to another using an intermediate variable, facilitating calculations where the original base is not standard.

  4. 10:00 – 15:00 10:00-15:00

    The instructor focuses on deriving and applying the Double Power Rule using the change of base formula. The general formula log_a^p(m^n) = n/p * log_a(m) is written in green on the board. A specific practice problem is presented: Find the value of log_10^2(100)^4. The instructor boxes this expression and uses arrows to show the cancellation of exponents, simplifying the complex logarithmic expression into a fraction involving n/p. The derivation demonstrates how to move from a complex base and argument structure to a simplified coefficient. This section reinforces the application of Property 6 through visual manipulation of exponents and algebraic simplification steps.

  5. 15:00 – 20:00 15:00-20:00

    The video segment covers the transition from complex logarithmic derivations to a new property. The instructor continues to demonstrate the simplification of expressions like log base a^p of m^n, emphasizing the n/p factor. The lesson moves towards concluding the mathematical derivations and preparing for the final property. Although specific visual details in this window are sparse, the progression indicates a consolidation of the Double Power Rule concepts before introducing the final identity. The instructor likely reviews the relationship between base powers and argument powers, ensuring students understand how to handle fractional exponents in logarithmic contexts.

  6. 20:00 – 21:21 20:00-21:21

    The video concludes with Property 8, the Active Passive Voice Rule. A slide displays the identity a^log b = b^log a, accompanied by images labeled 'Active Voice' and 'Passive Voice'. The instructor uses this grammatical analogy to illustrate how the base and exponent can swap positions in the logarithmic identity. The visual aid shows arrows indicating this swapping mechanism, connecting grammar concepts to mathematical rules. The segment ends with a 'Thanks for Watching' screen, marking the completion of the lecture on logarithmic properties. This final rule provides a unique mnemonic device for remembering a specific exponential-logarithmic identity.

The lecture systematically builds a comprehensive understanding of logarithmic properties, moving from basic power manipulation to complex base changes and unique identities. The Power Rule (Property 5) serves as the foundation, allowing exponents to be extracted from logarithmic arguments. This is rigorously proven through algebraic substitution, converting between logarithmic and exponential forms to validate the relationship. The Double Power Rule (Property 6) extends this concept, addressing scenarios where both the base and argument possess exponents. The instructor demonstrates that input powers become multipliers while base powers become reciprocals, resulting in a coefficient of n/p. This is further reinforced through the Base Changing Rule (Property 7), which enables conversion between different bases using an intermediate variable. The final property, the Active Passive Voice Rule (Property 8), offers a memorable identity where bases and exponents can be swapped in exponential-logarithmic expressions. Throughout the video, the instructor employs visual aids such as underlining, boxing, and arrows to highlight key components of formulas. Numerical examples, such as evaluating log_10(100)^2 and log_10^2(100)^4, provide concrete applications of the abstract rules. The teaching flow ensures that students grasp both the theoretical derivations and practical calculations required for mastering logarithmic manipulation.

Loading lesson…