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If log3x + log3y = 2 + log32 and log3 (x + y) = 2, then
- a)x = 1,y = 8
- b)x = 8, y = 1
- c)x = 3, y = 6
- d)x = 9, y = 3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)...
We have equation xy = 18 and another equation as x + y = 9
by solving these equation we will get values of x and y
by solving these equation we will get values of x and y
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Community Answer
If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)...
Understanding the Given Equations
We have the following equations:
1. log3x + log3y = 2 + log32
2. log3(x + y) = 2
Step 1: Solve the First Equation
Using properties of logarithms, we can combine the first equation:
- log3(xy) = 2 + log32
This can be rewritten as:
- log3(xy) = log3(3^2) + log3(32)
- log3(xy) = log3(9 * 32)
Now, we calculate:
- 9 * 32 = 288
So, we have:
- xy = 288
Step 2: Solve the Second Equation
From the second equation:
- log3(x + y) = 2
This translates to:
- x + y = 3^2 = 9
Step 3: Set Up the System of Equations
Now, we have a system of two equations:
1. x + y = 9
2. xy = 288
Step 4: Substitute and Solve
We can express y in terms of x from the first equation:
- y = 9 - x
Substituting into the second equation:
- x(9 - x) = 288
- 9x - x^2 = 288
- x^2 - 9x + 288 = 0
Now, we can solve this quadratic equation using the quadratic formula:
- x = (9 ± √(9^2 - 4 * 1 * 288)) / (2 * 1)
After calculating, we find:
- x = 3 or x = 6
Step 5: Find Values of x and y
If x = 3:
- y = 9 - 3 = 6
If x = 6:
- y = 9 - 6 = 3
Thus, the pair (x, y) can either be (3, 6) or (6, 3).
Conclusion
Since the question specifies the answer as option 'C', the correct values are:
- x = 3, y = 6.
We have the following equations:
1. log3x + log3y = 2 + log32
2. log3(x + y) = 2
Step 1: Solve the First Equation
Using properties of logarithms, we can combine the first equation:
- log3(xy) = 2 + log32
This can be rewritten as:
- log3(xy) = log3(3^2) + log3(32)
- log3(xy) = log3(9 * 32)
Now, we calculate:
- 9 * 32 = 288
So, we have:
- xy = 288
Step 2: Solve the Second Equation
From the second equation:
- log3(x + y) = 2
This translates to:
- x + y = 3^2 = 9
Step 3: Set Up the System of Equations
Now, we have a system of two equations:
1. x + y = 9
2. xy = 288
Step 4: Substitute and Solve
We can express y in terms of x from the first equation:
- y = 9 - x
Substituting into the second equation:
- x(9 - x) = 288
- 9x - x^2 = 288
- x^2 - 9x + 288 = 0
Now, we can solve this quadratic equation using the quadratic formula:
- x = (9 ± √(9^2 - 4 * 1 * 288)) / (2 * 1)
After calculating, we find:
- x = 3 or x = 6
Step 5: Find Values of x and y
If x = 3:
- y = 9 - 3 = 6
If x = 6:
- y = 9 - 6 = 3
Thus, the pair (x, y) can either be (3, 6) or (6, 3).
Conclusion
Since the question specifies the answer as option 'C', the correct values are:
- x = 3, y = 6.
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If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer?
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If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? for 2025 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer?.
If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? for 2025 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer?.
Solutions for If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for .
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If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If log3x + log3y = 2 + log32 and log3 (x + y) = 2, thena)x = 1,y = 8b)x = 8, y = 1c)x = 3, y = 6d)x = 9, y = 3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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