Question

$if \: {3}^{x + y } = 81 \: and \: {81}^{x - y} = 3$
then find the value of x and y​

Answer 1

Given:-

$★ \: \: \: {3}^{x + y } = 81$

$\implies \:{3}^{x + y} = {3}^{4}$

$\implies \bold{{x + y} = {4} \: \: - - - - (1)}$

And

$★ \: \: \: {81}^{x - y} = 3$

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

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

$\implies \: \bold {{4x - 4y} = 1 \: \: - - - (2)}$

{ We will solve those equations by Substituting Method }

† From eq (1) ,

x = 4 - y ------------(3)

Putting the value of x in eq(2) , we get

4(4-y) - 4y = 1

→ 16 - 4y - 4y = 1

→ 8y = 15

→ $\bold{\boxed{y \:\:=\frac{15}{8}}}$

Now, putting the value of y in eq(3) , we get,

$\: \: \: \: \bold {\rightarrow \: x = 4 - \frac{15}{8} }$

$\: \: \: \: \bold {\rightarrow \: x = \frac{32 - 15}{8} }$

$\: \: \: \boxed{ \bold {\rightarrow \: x = \frac{17}{8} }}$

Hence ,

★ x → 17/8

★ y →15/8

Answer 2

Answer:

x= 17/8 y=15/8 this is your answer