GATE 2018 - Computer Science - Logarithm - 2 Marks

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/TPSC-ASSISTANT-TECHNICAL-OFFICER/general-mental-ability-logical-reasoning/logarithm/solving-logarithmic-expressions-and-equations/asset-gate-2018-computer-science-logarithm-2-marks after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. 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
  9. 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, Unix OS, Linux OS
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: Introduction to CN, Data Communication, 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends, Internet of Things
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, 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, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
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.

Loading lesson…