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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Functions

BITSAT 2024 · Mathematics · Functions

Number of real solution of 5- _2|x| =3- _2|x| is equal to

Number of real solution of 5−log⁡2∣x∣=3−log⁡2∣x∣\sqrt{5-\log _2|x|}=3-\log _2|x| is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

 Let log⁡2∣x∣=t…(i)∴5−t=3−t⇒5−t=(3−t)2⇒5−t=9+t2−6t\begin{aligned} & \text{ Let } & \log _2|x| & =t \ldots(i)\\ & \therefore & \sqrt{5-t} & =3-t \\ \Rightarrow & & 5-t & =(3-t)^2 \\ \Rightarrow & & 5-t & =9+t^2-6 t \end{aligned}⇒t2−5t+4=0⇒(t−4)(t−1)=0⇒t=1 or 4[rejected][∵5−4=3−4,1≠−1]⇒log⁡2∣x∣=1⇒∣x∣=2⇒x=±2\begin{aligned} & \Rightarrow \quad t^2-5 t+4=0 \\ & \Rightarrow \quad(t-4)(t-1)=0 \\ & \Rightarrow \quad t=1 \text{ or } 4 \text{[rejected]}\\ & {[\because \sqrt{5-4}=3-4,1 \neq-1]} \\ & \Rightarrow \quad \log _2|x|=1 \\ & \Rightarrow \quad|x|=2 \\ & \Rightarrow \quad x= \pm 2 \end{aligned}\therefore$ Total 2 real solutions.
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