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If log x base 2 log x base 4 log x base 16 =21/4, find x.?
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If log x base 2 log x base 4 log x base 16 =21/4, find x.?
Solution:
Step 1: Simplifying the expression
We know that:
log a base b = log c base b / log c base a
Using this property, we can simplify the given expression as follows:
log x base 2 = log x base 4 / log 2 base 4
log x base 4 = log x base 16 / log 4 base 16
Substituting these values in the given expression, we get:
(log x base 4 / log 2 base 4) * (log x base 16 / log 4 base 16) = 21/4
Simplifying further, we get:
(log x base 2)^2 * (log x base 16) = 21/4
Step 2: Converting the logarithmic equation into exponential form
We can convert the above equation into exponential form as follows:
2^(log x base 2) * 16^(log x base 16) = 2^(21/4)
Simplifying further, we get:
x * x = 2^(21/4) * 2^(4/3)
x^2 = 2^(25/3)
x = (2^(25/3))^(1/2)
x = 2^(25/6)
Step 3: Final answer
Therefore, x = 2^(25/6) is the required solution.
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If log x base 2 log x base 4 log x base 16 =21/4, find x.?
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If log x base 2 log x base 4 log x base 16 =21/4, find x.? 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 log x base 2 log x base 4 log x base 16 =21/4, find x.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log x base 2 log x base 4 log x base 16 =21/4, find x.?.
If log x base 2 log x base 4 log x base 16 =21/4, find x.? 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 log x base 2 log x base 4 log x base 16 =21/4, find x.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log x base 2 log x base 4 log x base 16 =21/4, find x.?.
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