Question

Solve $2^{x+2}{27}^{x/(x-1)}=9$

• A. $x=1-\frac{\log 3}{\log 2}$
• B. $x=-2$
• C. $x=1-\frac{\log 2}{\log 3}$
• D. $x=2$

Answer 1

The correct option is B $x=-2$

$2^{x+2}{27}^{x/(x-1)}=9$
Taking log on both sides,
$(x+2){\log }_{e}2+\frac{x}{x-1}{\log }_{e}27={\log }_{e}9$
$(x+2){\log }_{e}2+\frac{3x}{x-1}{\log }_{e}3=2{\log }_{e}3$
$\Rightarrow (x+2){\log }_{e}2+\frac{(x+2)}{x-1}{\log }_{e}3=0$
$\Rightarrow (x+2)(x-1+\frac{{\log }_{e}3}{{\log }_{e}2})=0$
$\Rightarrow x=1-\frac{{\log }_{e}3}{{\log }_{e}2},x=-2$