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If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is?
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If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * ...
Solution:
Given,
1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c
Let's assume,
1/4 * log2 a = k
1/6 * log2 b = k
-1/24 * log2 c = k
Solving the above equations,
log2 a = 4k
log2 b = 6k
log2 c = -24k
Adding all three equations,
log2(a * b * c) = 4k + 6k - 24k
log2(a * b * c) = -14k
a * b * c = 2^(-14k) ........ (1)
Now,
a^3 * b^2 * c = (a * a * a) * (b * b) * c
Using equation (1),
a^3 * b^2 * c = (a * a * a) * (b * b) * c
a^3 * b^2 * c = (a^2 * b^2) * (a * c)
a^3 * b^2 * c = (a^2 * b^2) * (a * c) * (2^(-14k))
a^3 * b^2 * c = (a^2 * b^2 * c * a) * (2^(-14k))
a^3 * b^2 * c = (a^3 * b^2 * c) * (2^(-14k))
a^3 * b^2 * c / (a^3 * b^2 * c) = 2^(-14k)
a^0 * b^0 * c^0 = 2^(-14k)
1 = 2^(-14k)
2^(14k) = 1
2^k = 1/2^(14)
k = log2(1/2^(14))
k = -14/ log2(2)
k = -14
Therefore, a^3 * b^2 * c = 2^(-14k) = 2^(-14 * -14) = 2^196
Hence, a^3 * b^2 * c = 2^196.
Given,
1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c
Let's assume,
1/4 * log2 a = k
1/6 * log2 b = k
-1/24 * log2 c = k
Solving the above equations,
log2 a = 4k
log2 b = 6k
log2 c = -24k
Adding all three equations,
log2(a * b * c) = 4k + 6k - 24k
log2(a * b * c) = -14k
a * b * c = 2^(-14k) ........ (1)
Now,
a^3 * b^2 * c = (a * a * a) * (b * b) * c
Using equation (1),
a^3 * b^2 * c = (a * a * a) * (b * b) * c
a^3 * b^2 * c = (a^2 * b^2) * (a * c)
a^3 * b^2 * c = (a^2 * b^2) * (a * c) * (2^(-14k))
a^3 * b^2 * c = (a^2 * b^2 * c * a) * (2^(-14k))
a^3 * b^2 * c = (a^3 * b^2 * c) * (2^(-14k))
a^3 * b^2 * c / (a^3 * b^2 * c) = 2^(-14k)
a^0 * b^0 * c^0 = 2^(-14k)
1 = 2^(-14k)
2^(14k) = 1
2^k = 1/2^(14)
k = log2(1/2^(14))
k = -14/ log2(2)
k = -14
Therefore, a^3 * b^2 * c = 2^(-14k) = 2^(-14 * -14) = 2^196
Hence, a^3 * b^2 * c = 2^196.
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If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is? 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 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is?.
If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is? 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 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1/4 * log2 a = 1/6 * log2 b = - 1/24 * log2 c the value of a ^ 3 * b ^ 2 * c is?.
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