Question

If (3)to the power of (x +y) =81 and (81)to the power (x-y)=3 power of 8then the value of x and y are??

Answer 1

Answer:-

x= 3 , y = 1

Step - by - step explanation:-

According to the question

$\bf{ {3}^{(x + y)} = 81 }\\ \\ \bf{ {3}^{(x + y)} = {3}^{4} }$

Comparing power on both sides

→ x + y = 4 .........(1)

And ,

$\bf{ {81}^{(x - y)} = {3}^{8} } \\ \\ \bf{{3}^{4(x - y)} = {3}^{8} }$

Comparing power on both sides

Then we get,

→ 4(x - y )= 8

→ x - y = 2 ..........(2)

On adding equation (1) and (2)

2 x = 6

x = 3

Put x = 3 , in equation (2)

Then we get,

→3 - y = 2

→ y = 3 -2

y = 1

x = 3 ,y = 1

Hope it helps you.