JEE Exam > JEE Questions > Let m be the minimum possible value of log3 (...
Start Learning for Free
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.
Correct answer is '8.00'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where ...
Thus, log2 (m2) + log3 (m2) = 6 + 2 = 8
Most Upvoted Answer
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where ...
To find the minimum possible value of log3(3y1 3y2 3y3), we need to understand the properties of logarithms.
Firstly, we can rewrite the expression as log3(3y1) + log3(3y2) + log3(3y3).
Using the property of logarithms that states loga(b * c) = loga(b) + loga(c), we can simplify the expression to y1 * log3(3) + y2 * log3(3) + y3 * log3(3).
Since log3(3) = 1, the expression becomes y1 + y2 + y3.
Given that y1 + y2 + y3 = 9, the minimum possible value of the expression is 9.
Therefore, m = 9.
To find the maximum possible value of (log3x1 log3x2 log3x3), we can use a similar approach.
Rewriting the expression, we have log3(x1) + log3(x2) + log3(x3).
Using the property of logarithms loga(b * c) = loga(b) + loga(c), we can simplify the expression to log3(x1 * x2 * x3).
Since x1 * x2 * x3 = 9, the expression becomes log3(9).
Using the property of logarithms loga(b^c) = c * loga(b), we can rewrite the expression as 2 * log3(3).
Since log3(3) = 1, the expression simplifies to 2.
Therefore, M = 2.
To find the value of log2(m^3) log3(M^2), we substitute the values of m and M.
log2(m^3) = log2(9^3) = log2(729) = 9
log3(M^2) = log3(2^2) = log3(4) = 2
Therefore, the value of log2(m^3) log3(M^2) is 9 2 = 8.00.
Firstly, we can rewrite the expression as log3(3y1) + log3(3y2) + log3(3y3).
Using the property of logarithms that states loga(b * c) = loga(b) + loga(c), we can simplify the expression to y1 * log3(3) + y2 * log3(3) + y3 * log3(3).
Since log3(3) = 1, the expression becomes y1 + y2 + y3.
Given that y1 + y2 + y3 = 9, the minimum possible value of the expression is 9.
Therefore, m = 9.
To find the maximum possible value of (log3x1 log3x2 log3x3), we can use a similar approach.
Rewriting the expression, we have log3(x1) + log3(x2) + log3(x3).
Using the property of logarithms loga(b * c) = loga(b) + loga(c), we can simplify the expression to log3(x1 * x2 * x3).
Since x1 * x2 * x3 = 9, the expression becomes log3(9).
Using the property of logarithms loga(b^c) = c * loga(b), we can rewrite the expression as 2 * log3(3).
Since log3(3) = 1, the expression simplifies to 2.
Therefore, M = 2.
To find the value of log2(m^3) log3(M^2), we substitute the values of m and M.
log2(m^3) = log2(9^3) = log2(729) = 9
log3(M^2) = log3(2^2) = log3(4) = 2
Therefore, the value of log2(m^3) log3(M^2) is 9 2 = 8.00.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer?
Question Description
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer?.
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer?.
Solutions for Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer?, a detailed solution for Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? has been provided alongside types of Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let m be the minimum possible value of log3 ( 3y1 + 3y2+ 3y3) , where y1, y2, y3 are real numbers for which y1 + y2 + y3 = 9. Let M be the maximum possible value of (log3x1 + log3x2 + log3x3), where x1, x2 , x3 are positive real numbers for which x1 + x2 + x3 = 9. Then the value of log2 (m3) + log3(M2) is ______.Correct answer is '8.00'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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