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If log 16 log 2 a =log 4 b. then 2 ^b^2 is?
Most Upvoted Answer
If log 16 log 2 a =log 4 b. then 2 ^b^2 is?
Solution:
Given:
log 16 log 2 a = log 4 b
Solution Steps:
Step 1: Convert the given equation into exponential form
log a base b = x can be written as b^x = a
Using this formula, we can rewrite the given equation as:
(2^4)^log 2 a = (2^2)^log 4 b
Simplifying the above equation, we get:
2^(4log 2 a) = 2^(2log 4 b)
Step 2: Simplify the equation
Using the properties of logarithms, we can further simplify the equation as:
2^(2log 2 a) = b^2
2^(log (2a)^2) = b^2
2^(log 4a^2) = b^2
4a^2 = b^2
Step 3: Find 2^b^2
We need to find 2^b^2, which can be rewritten as 2^(2log b).
Using the given equation, we get:
log 16 log 2 a = log 4 b
2log 2 a = log 4 b
2(2log a base 2) = log 4 b
2log a base 2 = 1/2 log 4 b
2log a base 2 = log (4b)^1/2
2log a base 2 = log 2b
Taking exponentials on both sides, we get:
2^(2log a base 2) = 2^log 2b
a^2 = 2b
Substituting the value of b^2 in terms of a^2, we get:
4a^2 = (2a)^2
4a^2 = 4a^2
Therefore, 2^b^2 = 2^(2log b) = 2^(2log (a^2)) = 2^(log 4a^2) = 4a^2 = b^2
Final Answer:
Therefore, 2^b^2 = b^2 = 4a^2.
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If log 16 log 2 a =log 4 b. then 2 ^b^2 is?
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If log 16 log 2 a =log 4 b. then 2 ^b^2 is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log 16 log 2 a =log 4 b. then 2 ^b^2 is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log 16 log 2 a =log 4 b. then 2 ^b^2 is?.
If log 16 log 2 a =log 4 b. then 2 ^b^2 is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log 16 log 2 a =log 4 b. then 2 ^b^2 is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log 16 log 2 a =log 4 b. then 2 ^b^2 is?.
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