Some Important Log values to remember

Duration: 14 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 Yash Jain from Knowledge Gate Eduventures. The video begins with an introduction to logarithmic concepts, including the definition of a logarithm as the exponent to which a base must be raised to produce a given number, illustrated with the equation log_a(x) = y. It then transitions to a detailed discussion of logarithmic values, presenting two tables: one with exact values for base 10 logarithms (e.g., log 1 = 0, log 2 = 0.3010) and another with approximate values (e.g., log 2 ≈ 0.3, log 3 ≈ 0.5). The instructor explains how to use these approximate values to solve problems, demonstrating the application of logarithmic properties such as log(ab) = log a + log b and log(a/b) = log a - log b. The lecture includes a series of worked examples, such as calculating log 15 by breaking it down into log(3x5) = log 3 + log 5, and log 18 as log(2x3^2) = log 2 + 2log 3. The video concludes with a summary of the key points and a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying the word 'Logarithms' in large white text on a black background, with a hand writing 'log y =' on a chalkboard. This transitions to a collage of whiteboards with various logarithmic equations, such as 'log_a x = y' and 'log_2(8) = 3', and the text 'Logarithms' in a black oval. The instructor, Yash Jain, is visible in a small window, and the video is branded with 'KNOWLEDGE GATE EDUCATOR'. The instructor begins by explaining the fundamental concept of a logarithm, stating that if a^y = x, then log_a(x) = y, which is the exponent to which the base 'a' must be raised to get 'x'. He also introduces the terms 'base' and 'argument' in the context of logarithms.

  2. 2:00 – 5:00 02:00-05:00

    The video displays a slide titled 'Some Important log log Values' with a table of exact logarithmic values for base 10, ranging from log 1 to log 10. The instructor explains that these are the exact values, for example, log 2 = 0.3010 and log 3 = 0.4771. He then transitions to a new slide titled 'Exact Values to the base 10', which is a similar table. The instructor emphasizes the importance of memorizing these values. He then introduces a second table titled 'Approximate Values to the base 10', which simplifies the values (e.g., log 2 ≈ 0.3, log 3 ≈ 0.5). He explains that these approximate values are sufficient for solving problems quickly, especially in competitive exams, and that the exact values are provided for reference.

  3. 5:00 – 10:00 05:00-10:00

    The instructor begins to demonstrate how to use the approximate values to solve logarithmic problems. He starts with log 4, writing 'log 4 = log(2^2) = 2 log 2 = 2 x 0.3 = 0.6'. He then moves to log 6, writing 'log 6 = log(2x3) = log 2 + log 3 = 0.3 + 0.5 = 0.8'. He continues this process for log 8, log 9, and log 10, showing that log 8 = 0.9 and log 9 = 0.95. He also explains that log 11 is approximately 1.05. The instructor uses red circles and checkmarks to highlight the values and the correct answers, reinforcing the method of breaking down numbers into their prime factors and using the properties of logarithms.

  4. 10:00 – 14:10 10:00-14:10

    The video presents a new slide with a list of problems under the heading 'Que: Find the value of following'. The problems include log 15, log 24, log 18, log 48, log 1.5, and log(9/5). The instructor begins solving these problems using the approximate values. For log 15, he writes 'log 15 = log(3x5) = log 3 + log 5 = 0.5 + 0.7 = 1.2'. For log 18, he writes 'log 18 = log(2x3^2) = log 2 + 2 log 3 = 0.3 + 2(0.5) = 1.3'. For log 1.5, he writes 'log 1.5 = log(3/2) = log 3 - log 2 = 0.5 - 0.3 = 0.2'. For log(9/5), he writes 'log(9/5) = log 9 - log 5 = 2 log 3 - log 5 = 2(0.5) - 0.7 = 0.3'. The video concludes with a 'Thanks for Watching' screen.

The video provides a structured and practical lesson on logarithms, progressing from fundamental definitions to the application of approximate values for problem-solving. It effectively teaches students how to use the properties of logarithms to break down complex numbers into simpler components, making calculations faster and more efficient. The use of both exact and approximate value tables caters to different learning needs, while the worked examples demonstrate a clear, step-by-step methodology that is highly applicable to competitive exams.

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