The number of solutions of $\log_4 (x-1)

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The number of solutions of $\log_4 (x-1)=\log_2 (x-3)$, is _____.

Correct Answer:

Explanation:

For the given equation to be valid, we must have

$x-1 > 0$ and $x-3>0⇒x> 3$

Now,

$\log_4 (x-1)=\log_2 (x-3)$

$⇒\frac{1}{2}\log_2 (x-1)=\log_2 (x-3)$

$⇒\log_2 (x-1)=\log_2 (x-3)^2$

$⇒x-1=(x-3)^2$

$⇒x^2-7x+10=0⇒x=2,5⇒ x=5$ $[∵ x>3]$