Question

Need well explained answer

Answer 1

(3^2)^2x = 3^3/3^x+2
3^4x=3^3-x-2
4x=3-x-2
4x+x=1
5x=1
x=1/5 is answer

Answer 2

$\boxed{ Answer \: }$

$\implies { \: {9}^{2x} \: = \: \frac{27}{ {3}^{x \: + \: 2 } } } \\ \\ \implies \: ( \: {3}^{2} )^{2x} \: = \: \frac{ {3}^{3} }{ {3}^{x \: + \: 2} }$

$\boxed{\bold{ Algebric \: \: identities \: \: will \: be \: used \: }}$

$\boxed{ \implies \: \: ( {a}^{m} ) {}^{n} \: = \: {a}^{mn} \: }$

$\boxed{ \implies \: \frac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m \: - \: n} }$

$\bold{ Now, \: }$

$\implies \: {3}^{4x} \: = \: {3}^{ ( \: 3 \: - \: x \: - \: 2 \: )}$

$\implies \: {3}^{4x} \: = \: {3}^{( \: 1 \: - \: x \: )}$

$\bold{ On \: Comparison, }$

$\implies 4x \: = \: 1 \: - \: x \\ \\ \implies \: 4x \: + \: x \: = \: 1 \\ \\ \implies \: 5x \: = \: 1 \\ \\ \implies \: x \: = \frac{1}{5}$

$\bold{\boxed{ The \: \: required \: \: answer \: \: is \: \: \frac{1}{5} . }}$