Solved UPSC CDS/OTA Question
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Q · LogarithmMedium · 45s
For how many real values of x will the equation log₃log₆(x₃ – 18x₂ + 108x) = log₂log₄₁₆ be satisfied?
TopicLogarithm
Question Typemultiple choice
DifficultyMedium
Marking+1 / −0.33
Test Duration30 min
Step-by-Step Solution
The complete worked solution.
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Sol. log₂(log₄₁₆) = log₂log₄₄₂ = log₂₂ = 2
Log₃log₆(x₃ – 18x₂ + 108x) = 1
Log₆(x₃ – 18x₂ + 108x) = 3
x₃ – 18x₂ + 108x = 63
x₃ – 18x₂ + 108x – 216 = 0
(x – 6)3 = 0
x = 6 is the only value for which the above equation is true.
Final Answer: Option B - 5