Question

if 27^2x=9/3x find x

Answer 1

${27}^{2x} = 9 \div {3}^{x}$
${3}^{3 \times 2x} = {3}^{2} \div {3}^{x}$
${x}^{m} \div {x}^{n }\: = {x}^{m - n}$
${3}^{6x} = {3}^{2 - x}$
thus
$6x = 2 - x$
$7x = 2$
$x = 7 \div 2$