Question

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

• A. 3
• B. 1
• C. 2
• D. \N

Answer 1

The correct option is B 1

Given, $lo{g}_4(x-1)=lo{g}_2(x-3)=lo{g}_{4^{\frac{1}{2}}}(x-3)$
$\Rightarrow lo{g}_4(x-1)=lo{g}_4(x-3{)}^2\Rightarrow (x-3{)}^2=x-1\Rightarrow x^2+9-6x=x-1\Rightarrow x^2-7x+10=0$
$\Rightarrow (x-2)(x-5)=0\Rightarrow x=2,orx=5$
$\Rightarrow x=5[\because x=2$ makes log (x-3)undfined].
Hence, one solution exists.