If 27x + 2 ÷ ÷ 9x + 1 = 32x, find x

If 27x + 2 $÷$ 9x + 1 = 32x, find x

Answer Details

${27}^{x+2}÷9^{x+1}=3^{2x}$
Reduce 27 and 9 to have the same base as 3
$3^{3(x+2)}÷3^{2(x+1)}=3^{2x}$
Note, - is ÷ and + is × for powers of indices of the same bases.
$3^{3(x+2)-2(x+1)}=3^{2x}$
Equating the exponentials
$3(x+2)-2(x+1)=2x$
Clear brackets
$3x+6-2x-2=2x$
Collect like terms
$3x-2x-2x=-6+2$
$x-2x=-4$
$-x=-4$
Divide both sides by $-$
$x=4$
Answer is B