Question

Solve for $x$ :

$(\sqrt{3}{)}^{x-3}=(4\sqrt{3}{)}^{x+1}$

• A. $4$
• B. $7$
• C. $6$
• D. $8$

Answer 1

The correct option is B $7$

$\Rightarrow (\sqrt{3}{)}^{x-3}=(4\sqrt{3}{)}^{x+1}$
$\Rightarrow {\left({\left(3\right)}^{\frac{1}{2}}\right)}^{x-3}={\left({\left(3\right)}^{\frac{1}{4}}\right)}^{x+1}$
$\Rightarrow 3^{\frac{x-3}{2}}=3^{\frac{x+1}{4}}$
L H S and R H S base are same so we get a equation
$\Rightarrow \frac{x-3}{2}=\frac{x+1}{4}$

$\Rightarrow 4x-12=2x+2$
$\Rightarrow 4x-2x=2+12$
$\Rightarrow 2x=14$
$\Rightarrow x=7$