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If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)?
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If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)?
Solution:
Given, log (12) 27 = a
We need to find log (6) 16.
Let’s use the change of base formula:
log (12) 27 = log (6) 27 / log (6) 12
log (6) 16 = log (12) 16 / log (12) 6
Now, we need to find log (12) 16:
log (12) 16 = log (6) 16 / log (6) 12
log (12) 16 = (log (12) 27) (log (6) 12) / log (6) 12
log (12) 16 = a (log (12) 27) / (log (6) 12)
Substituting the value of log (12) 27 = a, we get:
log (12) 16 = a (1 + log (2) 3) / (1 + log (2) 2)
Now, we need to simplify the expression:
log (12) 16 = a (3 + log (2) 3) / (2 + log (2) 2)
log (12) 16 = a (3 + 1.585) / (2 + 0.693)
log (12) 16 = a (4.585 / 2.693)
log (12) 16 = a (1.703)
log (6) 16 = log (12) 16 / log (12) 6
log (6) 16 = a (1.703) / (1 + log (2) 2)
log (6) 16 = a (1.703) / (1 + 0.693)
log (6) 16 = a (1.703 / 1.693)
log (6) 16 = a (1.006)
Therefore, log (6) 16 = a (1.006) which is option (a) 4 (3-a/3 a).
Explanation:
We used the change of base formula to convert the given logarithms into a common base. Then, we simplified the expression and substituted the value of log (12) 27 = a. After simplifying, we obtained the value of log (6) 16, which is option (a) 4 (3-a/3 a).
Given, log (12) 27 = a
We need to find log (6) 16.
Let’s use the change of base formula:
log (12) 27 = log (6) 27 / log (6) 12
log (6) 16 = log (12) 16 / log (12) 6
Now, we need to find log (12) 16:
log (12) 16 = log (6) 16 / log (6) 12
log (12) 16 = (log (12) 27) (log (6) 12) / log (6) 12
log (12) 16 = a (log (12) 27) / (log (6) 12)
Substituting the value of log (12) 27 = a, we get:
log (12) 16 = a (1 + log (2) 3) / (1 + log (2) 2)
Now, we need to simplify the expression:
log (12) 16 = a (3 + log (2) 3) / (2 + log (2) 2)
log (12) 16 = a (3 + 1.585) / (2 + 0.693)
log (12) 16 = a (4.585 / 2.693)
log (12) 16 = a (1.703)
log (6) 16 = log (12) 16 / log (12) 6
log (6) 16 = a (1.703) / (1 + log (2) 2)
log (6) 16 = a (1.703) / (1 + 0.693)
log (6) 16 = a (1.703 / 1.693)
log (6) 16 = a (1.006)
Therefore, log (6) 16 = a (1.006) which is option (a) 4 (3-a/3 a).
Explanation:
We used the change of base formula to convert the given logarithms into a common base. Then, we simplified the expression and substituted the value of log (12) 27 = a. After simplifying, we obtained the value of log (6) 16, which is option (a) 4 (3-a/3 a).
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If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)?
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If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)?.
If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log (12) 27 =a then log (6) 16= (a)4 (3-a/3 a) (b)4 (3 a/3-a)?.
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