Question

Please tell me the answer along with an attachment.​

Answer 1

${ \bold{ \boxed{ \boxed{ \red{ \bigstar \: ANSWER}}}}}$

${ \bold{ \orange{ \mathtt{ : \implies \: {9}^{x + 2} = 240 + {9}^{x} }}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies {9}^{x + 2} - {9}^{x} = 240 }}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies \: {9}^{x} ( {9}^{2} - 1) = 240 }}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies {9}^{x}(81 - 1) = 240}}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies {9}^{x} (80) = 240}}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies \: {9}^{x} = 3}}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies {(3)}^{2x} = {(3)}^{1} }}}} \\ \\ { \bold{ \mathtt{ \blue{ \huge{now \: \: compare - }}}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies \: 2x = 1}}}} \\ \\ { \bold{ \orange{ \mathtt{ : \implies{ \boxed{x = \frac{1}{2} }}}}}}$