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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

The solution(s) of the equation 2 _3(x-2)+ _3(x-4)^2=0 , is/are

The solution(s) of the equation 2log⁡3(x−2)+log⁡3(x−4)2=02 \log _3(x-2)+\log _3(x-4)^2=0, is/are

Options

  1. A3+23+\sqrt{2}
  2. B3−23-\sqrt{2}
  3. C33
  4. D55

Correct answer

C. 33

Step-by-step solution

⇒log⁡((x−2)∣x−4∣)=0⇒(x−2)∣x−4∣=1\begin{aligned} & \Rightarrow \log ((x-2)|x-4|)=0 \\ & \Rightarrow(x-2)|x-4|=1\end{aligned} Case (I): x−4>0x-4\gt0⇒(x−2)(x−4)=1⇒x=3±2∵x≠3−2∴x=3+2\begin{aligned} & \Rightarrow(x-2)(x-4)=1 \\ & \Rightarrow x=3 \pm \sqrt{2} \\ & \because x \neq 3-\sqrt{2} \\ & \therefore x=3+\sqrt{2}\end{aligned}$\begin{aligned} & \text { Case (II): If, } x-4 \lt 0 \\ & \Rightarrow-(x-2)(x-4)=1 \\ & \Rightarrow x=3\end{aligned}
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