English, asked by chakrabortyranjita21, 3 months ago

if 3^(x+y) = 81 and 81^(x-y)= 3⁸ , then the find values of X and y respectively.

Answers

Answered by vaddinookaraju3
0

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Answered by Salmonpanna2022
7

Explanation:

\mathsf{Given : 3^{x + y} = 81}

\mathsf{\bigstar\;\;81\;can\;be\;written\;as : 3^4}

\mathsf{\implies 3^{x + y} = 3^4}

\bigstar\;\;\textsf{When Bases are same on both sides, Exponents should be equal}

\mathsf{\implies x + y = 4\;-----\;(1)}

\mathsf{Given : 81^{x - y} = 3^{8}}

\mathsf{\implies (3^4)^{x - y} = 3^{8}}

\mathsf{\implies 3^{4(x - y)} = 3^{8}}

\mathsf{\implies 4(x - y) = 8}

\mathsf{\implies (x - y) = \dfrac{8}{4}}

\mathsf{\implies x - y = 2\;-----\;(2)}

\textsf{Adding Equations (1) and (2), We get :}

\mathsf{\implies (x + y) + (x - y) = 4 + 2}

\mathsf{\implies x + x + y - y = 6}

\mathsf{\implies 2x = 6}

\mathsf{\implies x = 3}

\textsf{Substituting x = 3 in Equation (1), We get :}

\mathsf{\implies 3 + y = 4}

\mathsf{\implies y = 4 - 3}

\mathsf{\implies y = 1}

Answers :

★  x = 3

★  y = 1

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