Question

$\large{\bf{ \red{Que} \pink{st} \gray{ion}}}$

$\large{\sf{If \: {3}^{(x + y)} = 81 \: and \: {81}^{x - y} = 3 }}$
Find x and y​

Answer 1

Step-by-step explanation:

The camera angle marks the specific location at which the movie camera or video camera is placed to take a shot. A scene may be shot from several camera angles simultaneously. This will give a different experience and sometimes emotion.

correct answer in attachment

hope this helps you dear friend:)

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

$\rm \: {3}^{(x + y)} = 81$

$\rm \: {3}^{(x + y)} = {3}^{4}$

$\rm\implies \:x + y = 4 \: \cdots \: (1)$

Also, given that

$\rm \: {81}^{x - y} = 3$

$\rm \: { {(3}^{4} )}^{x - y} = 3$

$\rm \: {3}^{4x - 4y} = {3}^{1}$

$\rm\implies \:4x - 4y = 1$

$\rm \: 4x - 4(4 - x) = 1 \: \: \: \{ \: using \: (1) \: \}$

$\rm \: 4x -16 + 4x = 1 \:$

$\rm \: 8x = 16 + 1$

$\rm \: 8x = 17$

$\rm\implies \:\boxed{ \rm{ \:x = \dfrac{17}{8} \: }}$

On substituting the value of x in equation (1), we get

$\rm \: y + \dfrac{17}{8} = 4$

$\rm \: y = 4 - \dfrac{17}{8}$

$\rm \: y = \dfrac{32 - 17}{8}$

$\rm\implies \:\boxed{ \rm{ \:y \: = \: \frac{15}{8} \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{ {x}^{0} = 1}\\ \\ \bigstar \: \bf{ {x}^{m} \times {x}^{n} = {x}^{m + n} }\\ \\ \bigstar \: \bf{ {( {x}^{m})}^{n} = {x}^{mn} }\\ \\\bigstar \: \bf{ {x}^{m} \div {x}^{n} = {x}^{m - n} }\\ \\ \bigstar \: \bf{ {x}^{ - n} = \dfrac{1}{ {x}^{n} } }\\ \\\bigstar \: \bf{ {\bigg(\dfrac{a}{b} \bigg) }^{ - n} = {\bigg(\dfrac{b}{a} \bigg) }^{n} }\\ \\\bigstar \: \bf{ {x}^{m} = {x}^{n}\rm\implies \:m = n }\\ \\ \end{array} }}\end{gathered}\end{gathered}\end{gathered}$