Question

The equation $lo{g}_3\left(3^x-8\right)=2-x$ has the solution

• A. $x=1$
• B. $x=2$
• C. $x=3$
• D. $x=4$

Answer 1

Answer: (B)

$lo{g}_3\left(3^x-8\right)=2-x$
$\Rightarrow 3^x-8=3^{2-x},$ where $3^x-8>0$
$\Rightarrow 3^x-8=\frac{9}{3^x}$
$\Rightarrow {\left(3^x\right)}^2-8(3^x)-9=0$
$\Rightarrow \left(3^x+1\right)\left(3^x-9\right)=0$
$\Rightarrow 3^x=9\left[\because 3^x\ne -1\right]$
$\therefore x=2$