GATE 2018 - Computer Science - Logarithm - 2 Marks

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. Database Management System: 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
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. 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, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: 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
  10. 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
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a tutorial on solving a mathematical problem from the GATE CS 2018 exam. The problem presents three equations: p^(-x) = 1/q, q^(-y) = 1/r, and r^(-z) = 1/p, and asks for the value of the product xyz. The instructor, Yash Jain Sir, uses the logarithmic identity log(a^m) = m * log(a) to solve the problem. He takes the logarithm of both sides of each equation, which allows him to express x, y, and z in terms of logarithms of p, q, and r. He then multiplies these three expressions together, and through algebraic simplification, he shows that the product xyz equals 1. The video concludes with the instructor confirming the final answer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'GATE APTITUDE LOGARITHMS'. The main content begins with a problem displayed on a whiteboard: 'Q. If pqr ≠ 0 and p^(-x) = 1/q, q^(-y) = 1/r, r^(-z) = 1/p, what is the value of the product xyz? (GATE CS 2018) (2 MARKS)'. The instructor, Yash Jain Sir, introduces the problem and the four multiple-choice options: A. -1, B. 1/pqr, C. 1, D. pqr. He then begins to solve the problem by taking the logarithm of both sides of the first equation, p^(-x) = 1/q, which he writes as log(p^(-x)) = log(1/q). He applies the logarithmic rule log(a^m) = m * log(a) to get -x * log(p) = log(1/q). He then uses the rule log(1/a) = -log(a) to simplify the right side to -log(q). This gives him the equation -x * log(p) = -log(q), which he simplifies to x * log(p) = log(q). He then solves for x, writing x = log(q) / log(p). He proceeds to do the same for the second equation, q^(-y) = 1/r, to find y = log(r) / log(q). He then begins to work on the third equation, r^(-z) = 1/p, writing log(r^(-z)) = log(1/p) and simplifying to -z * log(r) = -log(p), which gives z = log(p) / log(r).

  2. 2:00 – 3:34 02:00-03:34

    The instructor now has the three expressions for x, y, and z: x = log(q) / log(p), y = log(r) / log(q), and z = log(p) / log(r). He states that the goal is to find the product xyz. He writes the product as (log(q) / log(p)) * (log(r) / log(q)) * (log(p) / log(r)). He then performs the multiplication, showing that the terms cancel out: the log(q) in the numerator of the first fraction cancels with the log(q) in the denominator of the second, the log(r) in the numerator of the second cancels with the log(r) in the denominator of the third, and the log(p) in the numerator of the third cancels with the log(p) in the denominator of the first. This leaves him with 1. He concludes that the product xyz is equal to 1. He then points to the multiple-choice options and confirms that the correct answer is C. 1. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a clear, step-by-step solution to a GATE exam problem using logarithmic properties. The core of the solution is the application of the logarithmic identity log(a^m) = m * log(a) to transform the given exponential equations into a form where the variables x, y, and z can be isolated. The final step is a clever algebraic simplification of the product xyz, where the intermediate terms cancel out, leading to the final answer of 1. The instructor's methodical approach demonstrates a powerful technique for solving systems of equations involving exponents.

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