Mathematics - Basic maths Question with Solution | TestHub

${\log }_4\left(x-1\right)={\log }_2\left(x-3\right)$

$\Rightarrow \frac{1}{2}{\log }_2\left(x-1\right)={\log }_2\left(x-3\right)$

$\Rightarrow {\log }_2{\left(x-1\right)}^{1/2}={\log }_2\left(x-3\right)$

$\Rightarrow {\left(x-1\right)}^{1/2}=x-3$

$\Rightarrow x-1=x^2+9-6x$

$\Rightarrow x^2-7x+10=0$

$\Rightarrow \left(x-2\right)\left(x-5\right)=0$

$\Rightarrow x=2,5$

But $x\ne 2$ because it is not satisfying the domain of given equation i.e ${\log }_2\left(x-3\right)\to$ its domain $x>3$ finally $x$ is $5$

$\therefore$ No. of solutions $=1$.