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If a + b + c = 0, A = 
and B = 3 abc, then find the value of logA(e2)-
and B = 3 abc, then find the value of logA(e2)-- a)1
- b)0
- c)2
- d)-1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-...
We know that when, a + b + c = 0 ; a3 + b3 + c3 = 3 abc
A = B
Now,
A = B
Now,
Hence, option 3.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-...
To find the value of logA(B^2), we need to substitute the given values of A and B into the expression and simplify it.
Given:
A = a^3 * b^3 * c^3
B = 3abc
Substituting the values of A and B into the expression:
logA(B^2) = log(a^3 * b^3 * c^3)((3abc)^2)
Simplifying the expression:
= log(a^3 * b^3 * c^3)(9a^2b^2c^2)
Using the properties of logarithms:
= log(a^3) + log(b^3) + log(c^3) + log(9a^2b^2c^2)
Applying the exponent rule of logarithms:
= 3log(a) + 3log(b) + 3log(c) + 2log(9) + 2log(a) + 2log(b) + 2log(c)
Combining like terms:
= 3log(a) + 3log(b) + 3log(c) + 2log(9) + 2log(a) + 2log(b) + 2log(c)
= 5log(a) + 5log(b) + 5log(c) + 2log(9)
Now, we are given that a * b * c = 0. This implies that at least one of the variables a, b, or c is zero.
If a, b, or c is zero, then log(a), log(b), or log(c) would be undefined (since logarithm of zero is undefined). Therefore, the given equation logA(B^2) cannot be evaluated.
Hence, the correct answer is option (c) - undefined.
Given:
A = a^3 * b^3 * c^3
B = 3abc
Substituting the values of A and B into the expression:
logA(B^2) = log(a^3 * b^3 * c^3)((3abc)^2)
Simplifying the expression:
= log(a^3 * b^3 * c^3)(9a^2b^2c^2)
Using the properties of logarithms:
= log(a^3) + log(b^3) + log(c^3) + log(9a^2b^2c^2)
Applying the exponent rule of logarithms:
= 3log(a) + 3log(b) + 3log(c) + 2log(9) + 2log(a) + 2log(b) + 2log(c)
Combining like terms:
= 3log(a) + 3log(b) + 3log(c) + 2log(9) + 2log(a) + 2log(b) + 2log(c)
= 5log(a) + 5log(b) + 5log(c) + 2log(9)
Now, we are given that a * b * c = 0. This implies that at least one of the variables a, b, or c is zero.
If a, b, or c is zero, then log(a), log(b), or log(c) would be undefined (since logarithm of zero is undefined). Therefore, the given equation logA(B^2) cannot be evaluated.
Hence, the correct answer is option (c) - undefined.
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If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer?
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If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer?.
If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a + b + c = 0, A = and B = 3 abc, then find the value of logA(e2)-a)1b)0c)2d)-1Correct answer is option 'C'. Can you explain this answer?.
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