Question

Number of solution(s) of ${\log }_2({4.3}^x-6)-{\log }_2(9^x-6)=1,$ is-

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

${\log }_2\left(\frac{{4.3}^x-6}{9^x-6}\right)=1$
$\left(\frac{{4.3}^x-6}{9^x-6}\right)=2$
Let $3^x=t$
$\Rightarrow 4t-6=2t^2-12$
$\Rightarrow 2t^2-4t-6=0$
$\Rightarrow t^2-2t-3=0$
$\Rightarrow (t-3)(t+1)=0$
$\Rightarrow 3^x=3\text{or}{3}^x=-1$
$\Rightarrow 3^x=3$ $\text{or}{3}^x=-1\text{(has no solution)}$
$\text{Hence,}x=1$