UPSC Exam > UPSC Questions > If log2X + log4X = log0.25√6 and x > 0, then...
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If log2X + log4X = log0.25√6 and x > 0, then x is
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If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithm...
Solution:
Given log2X log4X = log0.25√6 and x > 0
We know that,
loga (x) loga (y) = loga (x*y)
Therefore,
log2X log4X = log2X*4X = log8X^2
Now the given equation can be written as:
log8X^2 = log0.25√6
Converting RHS to base 8:
log8 (0.25√6) = log8 (0.25) + log8 (√6) = -1 + log8 (√6)
Therefore,
log8 X^2 = -1 + log8 (√6)
Taking antilog of both the sides:
X^2 = 8^(-1) * (√6)^8
X^2 = (√6)^(-1)
X = 1/√6
Hence, the value of x is 1/√6.
Given log2X log4X = log0.25√6 and x > 0
We know that,
loga (x) loga (y) = loga (x*y)
Therefore,
log2X log4X = log2X*4X = log8X^2
Now the given equation can be written as:
log8X^2 = log0.25√6
Converting RHS to base 8:
log8 (0.25√6) = log8 (0.25) + log8 (√6) = -1 + log8 (√6)
Therefore,
log8 X^2 = -1 + log8 (√6)
Taking antilog of both the sides:
X^2 = 8^(-1) * (√6)^8
X^2 = (√6)^(-1)
X = 1/√6
Hence, the value of x is 1/√6.
Community Answer
If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithm...
Log2x+log4x=log0.25√6
[log(a×b) =loga+logb]
log(2x×4x) =log0.25√6
from antilog-
2x×4x=0.25√6
8x=0.25√6
x=25√6÷800
x=√6÷32
x=0.0765
[log(a×b) =loga+logb]
log(2x×4x) =log0.25√6
from antilog-
2x×4x=0.25√6
8x=0.25√6
x=25√6÷800
x=√6÷32
x=0.0765
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If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude?
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If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude?.
If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log2X + log4X = log0.25√6 and x > 0, then x is Related: Logarithms - Important Formulas, Quantitative Aptitude?.
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