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Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals
(2019)
- a)12
- b)13
- c)14
- d)15
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let f be a function such that f(mn) = f(m) f(n) for every positive int...
Let the value of f(2) and f(3) be ‘x’ and ‘y’ respectively,
⇒ f(24) = f(8).f(3) = f(2).f(2).f(2).f(3) = 54
⇒ x3y = 54
⇒ x3y = 27 × 2
⇒ x3y = 33 × 2
On comparing, x = 3 and y = 2
⇒ f(2) = 3
⇒ f(3) = 2
⇒ f(18) = f(9).f(2) = f(3).f(3).f(2)
⇒ f(18) = 2 × 2 × 3
⇒ f(18) = 12
∴ The value of f(18) equals 12
Most Upvoted Answer
Let f be a function such that f(mn) = f(m) f(n) for every positive int...
To find the value of f(1), we can use the given property of the function for any positive integer n.
Let's consider n = 1:
f(1*1) = f(1) f(1)
Since f(1*1) = f(1), we have:
f(1) = f(1) f(1)
Dividing both sides by f(1), we get:
1 = f(1)
Therefore, f(1) = 1.
Now, let's find the value of f(2):
Using the property of the function, we have:
f(2*1) = f(2) f(1)
Since f(2*1) = f(2), we have:
f(2) = f(2) f(1)
Dividing both sides by f(2), we get:
1 = f(1)
We already know that f(1) = 1, so we can substitute this value:
1 = 1 * f(1)
1 = 1
Therefore, f(2) can be any positive integer.
Finally, let's find the value of f(3):
Using the property of the function, we have:
f(3*1) = f(3) f(1)
Since f(3*1) = f(3), we have:
f(3) = f(3) f(1)
Dividing both sides by f(3), we get:
1 = f(1)
We already know that f(1) = 1, so we can substitute this value:
1 = 1 * f(3)
1 = f(3)
Therefore, f(3) = 1.
In summary, we found that f(1) = 1, f(2) can be any positive integer, and f(3) = 1.
Let's consider n = 1:
f(1*1) = f(1) f(1)
Since f(1*1) = f(1), we have:
f(1) = f(1) f(1)
Dividing both sides by f(1), we get:
1 = f(1)
Therefore, f(1) = 1.
Now, let's find the value of f(2):
Using the property of the function, we have:
f(2*1) = f(2) f(1)
Since f(2*1) = f(2), we have:
f(2) = f(2) f(1)
Dividing both sides by f(2), we get:
1 = f(1)
We already know that f(1) = 1, so we can substitute this value:
1 = 1 * f(1)
1 = 1
Therefore, f(2) can be any positive integer.
Finally, let's find the value of f(3):
Using the property of the function, we have:
f(3*1) = f(3) f(1)
Since f(3*1) = f(3), we have:
f(3) = f(3) f(1)
Dividing both sides by f(3), we get:
1 = f(1)
We already know that f(1) = 1, so we can substitute this value:
1 = 1 * f(3)
1 = f(3)
Therefore, f(3) = 1.
In summary, we found that f(1) = 1, f(2) can be any positive integer, and f(3) = 1.
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Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. Can you explain this answer?
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Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. 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 Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. Can you explain this answer?.
Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. 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 Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals(2019)a)12b)13c)14d)15Correct answer is option 'A'. Can you explain this answer?.
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