GATE 2018 - Computer Science - Logarithm - 2 Marks

Duration: 4 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. Numerical Ability & Problem Solving: Speed Mathematics and Basic Mathematics, Arithmetic, Number System, HCF LCM, Divisibility Rules, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Time and Work, Pipe and Cistern, Speed Time and Distance, Age Problems, Partnership, Data Interpretation, Mental Ability, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Algebra, Statistics, Logarithm, Mensuration and Geometry, Permutation and Combination, Probability, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Sentence Structure and Correction, Data Sufficiency, Trigonometry, Measurement and Quantity Take-Off, Signal Space and Optimum Detection, Probability, Statistics, Algebra, Time and Work, Speed, Time and Distance, Data Interpretation, Combinatorics
  2. Logical 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), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Logical Sequence Of Words, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Selection Decision Table (Decision Making), Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Logical Deduction and Induction, Syllogisms and Venn Diagrams, Critical Reasoning, Order, Ranking and Sequence, Reading Comprehension, Profit, Loss and Discount, Constraint Puzzles, Traverse Surveying, Ratio and Proportion, Mensuration, Permutations and Combinations, Clocks and Calendars, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Vocabulary, Blood Relations
  3. General Knowledge & Current Affairs (India + Rajasthan): History, Geography, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs, Environment, Physics
  4. Computer Fundamentals & Operating Systems: Basics of COA, Floating Point Rep, Digital Systems & Boolean Basics, Number Representation, Number System, Introduction to OS, File Management, Windows OS, Unix OS, Linux OS, Register Transfer and Microoperations, Virtual Memory
  5. Computer Networks: Introduction to CN, Data Communication, DLL: Error Control, DLL: Access Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Application Layer, Hardware Basics, Network Security
  6. Cyber Security: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  7. Programming (C & OOP): C Fundamentals, Control Flow, Arrays & Pointers, Functions, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Operators & Expressions, Sorting Algorithms, Java Fundamentals, Java
  8. MS Office & Data Processing: MS Office Applications, Basics of DBMS
  9. Internet & Web Technology: Society, Law & Ethics, Terms & Abbreviations, Keyboard Shortcuts, Emerging Tech Trends, Artificial Intelligence, Emerging Technologies, Internet Fundamentals, Website, Browser & Services, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security
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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