Set 1 - Important Questions on Logarithms

Duration: 12 min

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Module outline

  1. About Course: About the Course
  2. Paper 1 | Quantitative Aptitude: Speed Mathematics and Basic Mathematics, Percentage, Ratio and Proportion (Ratios), Powers and Exponents (Surds and Indices), Logarithm, Sequence and Series (Series), Mensuration and Geometry, Data Interpretation, Average, Arithmetic
  3. Paper 1 | Logical Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Analogy, Cubes & Dices, Syllogisms
  4. Paper 1 | English Language: Vocabulary, Noun, Pronoun, Verb, Adjectives, Adverb, Preposition, Conjunction, Interjection, Articles, Tenses, Subject Verb Agreement (Verb Noun Agreement), Modals, Determiner, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Construction
  5. Paper 1 | Unit Tests:
  6. Paper 1 | Full-Length Mock Tests:
  7. Paper 2 | Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Permutation and Combination, Probability, Statistics
  8. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Paper 2 | Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  10. Paper 2 | Programming and Data Structures: 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
  11. Paper 2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  12. Paper 2 | Theory Of Computation/Automata Theory: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  13. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  14. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  15. Paper 2 | DataBase Management System/DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery
  16. Paper 2 | Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  17. Paper 2 | CS/IT Sectional Mock Tests:
  18. Complete Paper Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a comprehensive lecture on logarithms, presented by an instructor from Knowledge Gate Educator. The video begins with an introduction to the topic, displaying the word 'Logarithms' and a hand writing 'log y ='. It then transitions into a series of problem-solving sessions, starting with a title slide for 'Important Questions on Logarithms Set 1'. The core of the video consists of the instructor solving various logarithmic expressions, such as log₂3, log₂₅27, and log₄9, using the change of base formula, log_b(a) = log a / log b. The instructor demonstrates how to simplify these expressions by expressing the arguments as powers of the base, for example, rewriting log₂₅27 as log₁₀(3³) / log₁₀(5²), which simplifies to 3log₁₀3 / 2log₁₀5. The video also covers more complex problems, including log₁₀81, log₃√3, and log₂32, using properties like log(a^b) = b*log(a) and log(a/b) = log a - log b. The instructor provides step-by-step solutions, often using approximate values for common logs (e.g., log₁₀2 ≈ 0.3, log₁₀3 ≈ 0.48) to calculate final numerical answers. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card featuring the word 'Logarithms' and a hand writing 'log y ='. It then transitions to a collage of whiteboards with various logarithmic equations, including 'log_a x = y', 'a^y = x', and 'log₂(8) = 3'. The instructor, Yash Jain, is visible in a small window, and the video is branded as 'Knowledge Gate Educator'. The main title slide appears, stating 'Important Questions on Logarithms Set 1', with a background image of a teacher and student at a chalkboard with the equation 'log₂(x²-6x) - log₂(1-x) = 3'. The instructor begins to explain the topic, with the text 'Logarithm Questions and Answers' displayed.

  2. 2:00 – 5:00 02:00-05:00

    The video presents a series of problems under the heading 'Que: Find the value of following (Set1)'. The first problem is log₂3. The instructor writes the change of base formula, log_b(a) = log a / log b, and substitutes the values, writing log₁₀3 / log₁₀2. He then uses approximate values, 0.48 / 0.3, and simplifies it to 48/30, which reduces to 16/10, resulting in 1.6. The next problem is log₂₅27. The instructor rewrites it as log₁₀(3³) / log₁₀(5²), which becomes 3log₁₀3 / 2log₁₀5. He then substitutes the values, 3*0.48 / 2*0.7, and calculates the result as 1.44 / 1.4, which simplifies to 1.02857. The third problem is log₄9. The instructor rewrites it as log₁₀(3²) / log₁₀(2²), which becomes 2log₁₀3 / 2log₁₀2. He simplifies this to log₁₀3 / log₁₀2, which is the same as the first problem, resulting in 1.6.

  3. 5:00 – 10:00 05:00-10:00

    The video continues with more logarithmic problems. The first is log₁₀81. The instructor rewrites it as log₁₀(3⁴), which becomes 4log₁₀3. He substitutes the value 0.48, resulting in 4*0.48 = 1.92. The next problem is log₃√3. The instructor rewrites √3 as 3^(1/2), so the expression becomes log₃(3^(1/2)), which simplifies to 1/2. The third problem is log₂32. The instructor rewrites 32 as 2⁵, so the expression becomes log₂(2⁵), which simplifies to 5. The fourth problem is log₁₅27√3. The instructor rewrites 27√3 as 3³ * 3^(1/2) = 3^(7/2), so the expression becomes log₁₅(3^(7/2)). He then uses the change of base formula, log₁₀(3^(7/2)) / log₁₀(15), which becomes (7/2)log₁₀3 / (log₁₀3 + log₁₀5). He substitutes the values, (7/2)*0.48 / (0.48 + 0.7), and calculates the result as 1.68 / 1.18, which simplifies to 1.4237. The final problem is log₃(1/243). The instructor rewrites 1/243 as 3^(-5), so the expression becomes log₃(3^(-5)), which simplifies to -5.

  4. 10:00 – 12:02 10:00-12:02

    The video presents the final problem, log₁₀0.1. The instructor rewrites 0.1 as 10^(-1), so the expression becomes log₁₀(10^(-1)), which simplifies to -1. The next problem is log₆216. The instructor rewrites 216 as 6³, so the expression becomes log₆(6³), which simplifies to 3. The final problem is log₂81. The instructor rewrites 81 as 3⁴, so the expression becomes log₂(3⁴), which becomes 4log₂3. He then uses the change of base formula, 4 * (log₁₀3 / log₁₀2), and substitutes the values, 4 * (0.48 / 0.3), which simplifies to 4 * 1.6 = 6.4. The video concludes with a 'Thanks for Watching' screen.

The video provides a structured and methodical approach to solving logarithmic problems. It begins by establishing the fundamental concept of the change of base formula, which is the cornerstone for solving all the problems. The instructor then systematically applies this formula to a variety of expressions, demonstrating how to simplify them by expressing the arguments as powers of the base. The use of approximate values for common logarithms (log₁₀2 and log₁₀3) allows for the calculation of numerical answers, making the concepts more tangible. The progression from simple problems like log₂3 to more complex ones like log₁₅27√3 shows a clear increase in difficulty, helping students build confidence. The video effectively combines theory with practical application, making it a valuable resource for students preparing for exams that test logarithmic skills.

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