GATE 2018 - Computer Science - Logarithm - 2 Marks
Duration: 4 min
This video lesson is available to enrolled students.
Inside: a video lesson and guided study material.
Module outline
- Aptitude: 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, Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, TCS NQT Advanced Quantitative Ability, Speed Mathematics and Basic Mathematics, Arithmetic, Statistics, Partnership, Age Problems, Mental Ability, Mensuration and Geometry, Linear Algebra, Calculus, Trigonometry, Vectors, Gamified / Game Based Aptitude
- Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, TCS NQT Advanced Reasoning Ability, Ranking, Order and Sequence, Analogy, Inequality, Data Arrangement, Venn Diagram, Logical Sequence Of Words, Selection Decision Table (Decision Making), Cubes & Dices, Clock, Calendar, Puzzle Solving (Puzzles), Analytical Reasoning (Counting Figures Reasoning), Directions (Direction Test), Blood Relations, Seating Arrangements
- Verbal Ability (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Articles, Direct and Indirect Speech, Conjunction, 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, Verb
- Mega Test:
- Grand 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
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).
2:00 – 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.