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

The correct option is B $1$

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

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

${log}_2(x-1)=2{log}_2(x-3)$

${log}_2(x-1)={log}_2{(x-3)}^2$

$x-1={(x-3)}^2$

$x^2-6x+9-x+1=0$

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

$(x-5)(x-2)=0$

$x=5$ $x=2$ (not possible)

$log(-1)$ is not defined)

No. of solution $=1$.