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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

Let | _ 2 30-| _2 9+| _4 9-| _ 1/2 5||||=x . Then the smallest...

Let ∣log⁡230−∣log⁡29+∣log⁡49−∣log⁡1/25∣∣∣∣=x\left|\log _{\sqrt{2}} 30-\right| \log _2 9+\left|\log _4 9-\right| \log _{1/2} 5||||=x. Then the smallest integer greater than or equal to xx, is:

Correct answer

6

Step-by-step solution

∣log⁡230−∣log⁡29+∣log⁡23−log⁡25∣∣∣=∣log⁡230−∣log⁡29+log⁡25−log⁡23∣∣=∣log⁡230−∣log⁡23+log⁡25∣∣=∣log⁡230−log⁡215∣=log⁡2605<log⁡260<6\begin{aligned} & \left|\log _{\sqrt{2}} 30-\right| \log _2 9+\left|\log _2 3-\log _2 5\right|||=\left|\log _{\sqrt{2}} 30-\right| \log _2 9+\log _2 5-\log _2 3|| \\ & =\left|\log _{\sqrt{2}} 30-\right| \log _2 3+\log _2 5||=\left|\log _{\sqrt{2}} 30-\log _2 15\right|=\log _2 60 \\ & 5 < \log _2 60 < 6\end{aligned}
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