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If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these?
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If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c...
Solution:
Given, log2 x + log4 x + log16x = 21/4
We know that, loga (x) + loga (y) = loga (xy) and loga (x) + logb (x) = loga*b (x)
Therefore, we can rewrite the given equation as:
log2 x + log4 x + log16x = log2 x + 2log2 x + 4log2 x = 7log2 x
Thus, the equation becomes:
7log2 x = 21/4
log2 x = 3/4
Now, we can rewrite this equation in exponential form as:
x = 2^(log2 x) = 2^(3/4)
x = √(2^3)
x = √8
x = 2√2
Hence, the correct answer is (d) none of these.
Explanation:
- Given equation is transformed using log laws.
- The equation is simplified using the properties of logarithms.
- The equation is further simplified to get the value of log2 x.
- Finally, the value of x is obtained using exponential form.
- The correct answer is obtained after simplification.
Given, log2 x + log4 x + log16x = 21/4
We know that, loga (x) + loga (y) = loga (xy) and loga (x) + logb (x) = loga*b (x)
Therefore, we can rewrite the given equation as:
log2 x + log4 x + log16x = log2 x + 2log2 x + 4log2 x = 7log2 x
Thus, the equation becomes:
7log2 x = 21/4
log2 x = 3/4
Now, we can rewrite this equation in exponential form as:
x = 2^(log2 x) = 2^(3/4)
x = √(2^3)
x = √8
x = 2√2
Hence, the correct answer is (d) none of these.
Explanation:
- Given equation is transformed using log laws.
- The equation is simplified using the properties of logarithms.
- The equation is further simplified to get the value of log2 x.
- Finally, the value of x is obtained using exponential form.
- The correct answer is obtained after simplification.
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If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these?
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If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (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 If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these?.
If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (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 If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log2 x log4 x log16x = 21/4, these x is equal to (a) 8 (b) 4 (c) 16 (d) none of these?.
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