CAT Exam > CAT Questions > Find the value of [log2100]+[log399]+[log498]...
Start Learning for Free
Find the value of [log2 100]+[log3 99]+[log4 98]+[log5 97]+....+[log100 2] where [X] equals the largest integer less than or equal to X.
Correct answer is '65'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2]...
[log2 100] = 6 since 26 = 64
Similarly,
[log3 99] = 4
[log4 98] = 3
From [log5 97] to [log9 93], we get 2 each.
From [log10 92] to [log51 51], we get 1. For the rest we get 0.
Hence, sum = 6 + 4 + 3 + 5 x 2 + 42 x 1 = 65
Similarly,
[log3 99] = 4
[log4 98] = 3
From [log5 97] to [log9 93], we get 2 each.
From [log10 92] to [log51 51], we get 1. For the rest we get 0.
Hence, sum = 6 + 4 + 3 + 5 x 2 + 42 x 1 = 65
Most Upvoted Answer
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2]...
Explanation:
To find the value of [log2100] [log399] [log498] [log597] .... [log100 2], we need to find the largest integer less than or equal to the logarithm of each number and then multiply them together.
Let's break down the solution step by step:
Step 1: Calculate the logarithm of each number
- [log2100] = log2(100) = 6.64 (approx.)
- [log399] = log3(99) = 4.62 (approx.)
- [log498] = log4(98) = 3.93 (approx.)
- [log597] = log5(97) = 3.14 (approx.)
- [log696] = log6(96) = 2.75 (approx.)
- [log795] = log7(95) = 2.38 (approx.)
- [log894] = log8(94) = 2.04 (approx.)
- [log993] = log9(93) = 1.72 (approx.)
- [log1092] = log10(92) = 1.42 (approx.)
- [log1191] = log11(91) = 1.14 (approx.)
- [log1290] = log12(90) = 0.88 (approx.)
- [log1389] = log13(89) = 0.64 (approx.)
- [log1488] = log14(88) = 0.42 (approx.)
- [log1587] = log15(87) = 0.20 (approx.)
- [log1686] = log16(86) = 0 (since log16(86) is less than 1)
Step 2: Find the largest integer less than or equal to each logarithm
- [log2100] = 6
- [log399] = 4
- [log498] = 3
- [log597] = 3
- [log696] = 2
- [log795] = 2
- [log894] = 2
- [log993] = 1
- [log1092] = 1
- [log1191] = 1
- [log1290] = 0
- [log1389] = 0
- [log1488] = 0
- [log1587] = 0
- [log1686] = 0
Step 3: Multiply the obtained values together
6 * 4 * 3 * 3 * 2 * 2 * 2 * 1 * 1 * 1 * 0 * 0 * 0 * 0 * 0 = 0
Therefore, the value of [log2100] [log399] [log498] [log597] .... [log100 2] is 0.
To find the value of [log2100] [log399] [log498] [log597] .... [log100 2], we need to find the largest integer less than or equal to the logarithm of each number and then multiply them together.
Let's break down the solution step by step:
Step 1: Calculate the logarithm of each number
- [log2100] = log2(100) = 6.64 (approx.)
- [log399] = log3(99) = 4.62 (approx.)
- [log498] = log4(98) = 3.93 (approx.)
- [log597] = log5(97) = 3.14 (approx.)
- [log696] = log6(96) = 2.75 (approx.)
- [log795] = log7(95) = 2.38 (approx.)
- [log894] = log8(94) = 2.04 (approx.)
- [log993] = log9(93) = 1.72 (approx.)
- [log1092] = log10(92) = 1.42 (approx.)
- [log1191] = log11(91) = 1.14 (approx.)
- [log1290] = log12(90) = 0.88 (approx.)
- [log1389] = log13(89) = 0.64 (approx.)
- [log1488] = log14(88) = 0.42 (approx.)
- [log1587] = log15(87) = 0.20 (approx.)
- [log1686] = log16(86) = 0 (since log16(86) is less than 1)
Step 2: Find the largest integer less than or equal to each logarithm
- [log2100] = 6
- [log399] = 4
- [log498] = 3
- [log597] = 3
- [log696] = 2
- [log795] = 2
- [log894] = 2
- [log993] = 1
- [log1092] = 1
- [log1191] = 1
- [log1290] = 0
- [log1389] = 0
- [log1488] = 0
- [log1587] = 0
- [log1686] = 0
Step 3: Multiply the obtained values together
6 * 4 * 3 * 3 * 2 * 2 * 2 * 1 * 1 * 1 * 0 * 0 * 0 * 0 * 0 = 0
Therefore, the value of [log2100] [log399] [log498] [log597] .... [log100 2] is 0.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer?
Question Description
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer?.
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer?.
Solutions for Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer?, a detailed solution for Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? has been provided alongside types of Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup