Quant Exam > Quant Questions > What is the value o f log32 - log43.log54...l...
Start Learning for Free
What is the value o f log32 - log43.log54...log1615?
- a)1/2
- b)1/3
- c)2/3
- d)1/4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1...
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1...
Calculation of log values
- log32 = log(2^5) = 5log2
- log43 = log(3^4) = 4log3
- log54 = log(2^7) = 7log5
- ...
- log1615 = log(15^16) = 16log15
Substitute log values
Substitute the log values into the expression log32 - log43.log54...log1615:
= 5log2 - 4log3 - 7log5 - ... - 16log15
Use logarithmic properties
Apply the logarithmic property log(a) - log(b) = log(a/b):
= log(2^5) - log(3^4) + log(5^7) + ... + log(15^16)
= log(2^5 * 5^7 * ... * 15^16)
= log(2^5 * 3^0 * 4^0 * ... * 15^0)
= log(2^5)
= 5log2
Final answer
Therefore, the value of log32 - log43.log54...log1615 is 5log2, which simplifies to log(2^5) = log(32) = 5log2 = 1/4. Hence, the correct answer is option 'D' (1/4).
- log32 = log(2^5) = 5log2
- log43 = log(3^4) = 4log3
- log54 = log(2^7) = 7log5
- ...
- log1615 = log(15^16) = 16log15
Substitute log values
Substitute the log values into the expression log32 - log43.log54...log1615:
= 5log2 - 4log3 - 7log5 - ... - 16log15
Use logarithmic properties
Apply the logarithmic property log(a) - log(b) = log(a/b):
= log(2^5) - log(3^4) + log(5^7) + ... + log(15^16)
= log(2^5 * 5^7 * ... * 15^16)
= log(2^5 * 3^0 * 4^0 * ... * 15^0)
= log(2^5)
= 5log2
Final answer
Therefore, the value of log32 - log43.log54...log1615 is 5log2, which simplifies to log(2^5) = log(32) = 5log2 = 1/4. Hence, the correct answer is option 'D' (1/4).
|
|
Explore Courses for Quant exam
|
|
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer?
Question Description
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer?.
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the value o f log32 - log43.log54...log1615?a)1/2b)1/3c)2/3d)1/4Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup