# If 3^(x+y) =81 and 81^(x-y)=3, then the value of x/y is

(a) 15/34

(b) 15/17

(c) 17/15

(d) 17/30

**Answer: (c) 17/15**

**Solution:-**

3^(x + y) = 81

3^(x + y) = 3^4

Comparing on both side,

X + Y = 4 ………….. (1)

81^(x – y) = 3

3^4(x – y) = 3^1

Comparing on both side,

4 x – 4 y = 1 …………… (2)

In equation(1) multiply by 4,

Then, 4 X + 4 Y = 16 …………. (3)

Add equation (1) & (2),

Then, 4 X – 4 Y + 4 X + 4 Y = 16 + 1

8 X = 17

X = 17/8

Put the value of X = 17/8 equation (1),

17/8 + Y = 4

Y = 4 – 17/8

Y = (32 – 17)/8

Y = 15/8

Then, the ratio of X/Y = 17 x 8/15 x 8

= 17/15

Hence, the correct answer is option (c) 17/15.