Question

The number of solutions of $lo{g}_4(x+1)=lo{g}_2(x-3)$ is

• A. 3
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (B)

${\log }_4(x-1)={\log }_2(x-3)$
$\Rightarrow {\log }_4(x-1)=2{\log }_4(x-3)$
$\Rightarrow {\log }_4(x-1)={\log }_4(x-3{)}^2$
$\Rightarrow x-1=x^2+9-6x$
$\Rightarrow x^2-7x+10=0$
$\Rightarrow (x-5)(x-2)=0$
$\Rightarrow x=5$ or $2$
Hence, $x=5\{\because x=2$ makes $\log (x-3)$ undefined $\}$
$\therefore$ Number of solution is $1.$