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6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these?
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6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none ...
Solution:
To solve the equation 2 log x = 4 log 3, we need to apply the properties of logarithms.
Properties of logarithms:
1. log a + log b = log (a * b)
2. log a - log b = log (a / b)
3. log a^n = n log a
Step 1: Simplify the equation using the properties of logarithms.
2 log x = 4 log 3
Using property 3, we can rewrite the equation as:
log x^2 = log 3^4
Step 2: Remove the logarithms from both sides of the equation.
x^2 = 3^4
Simplifying further, we have:
x^2 = 81
Step 3: Solve for x by taking the square root of both sides.
x = ±√(81)
Taking the square root, we get:
x = ±9
Since the equation does not specify any restrictions on x, both x = 9 and x = -9 are valid solutions.
Step 4: Determine which option (a), (b), (c), or (d) matches the solutions.
(a) 3: x = 3 is not a solution.
(b) 9: x = 9 is a solution.
(c) 2: x = 2 is not a solution.
(d) none of these: x = -9 is a solution.
Therefore, the correct answer is (b) 9.
To solve the equation 2 log x = 4 log 3, we need to apply the properties of logarithms.
Properties of logarithms:
1. log a + log b = log (a * b)
2. log a - log b = log (a / b)
3. log a^n = n log a
Step 1: Simplify the equation using the properties of logarithms.
2 log x = 4 log 3
Using property 3, we can rewrite the equation as:
log x^2 = log 3^4
Step 2: Remove the logarithms from both sides of the equation.
x^2 = 3^4
Simplifying further, we have:
x^2 = 81
Step 3: Solve for x by taking the square root of both sides.
x = ±√(81)
Taking the square root, we get:
x = ±9
Since the equation does not specify any restrictions on x, both x = 9 and x = -9 are valid solutions.
Step 4: Determine which option (a), (b), (c), or (d) matches the solutions.
(a) 3: x = 3 is not a solution.
(b) 9: x = 9 is a solution.
(c) 2: x = 2 is not a solution.
(d) none of these: x = -9 is a solution.
Therefore, the correct answer is (b) 9.
Community Answer
6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none ...
And 9
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6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these?
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6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these?.
6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 6. If 2 log x = 4 log 3, the x is equal to (a) 3 (b) 9 (c) 2 (d) none of these?.
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