If x^y = 2^12 (1) and y^(x-2) = 2^12 (2) then x/y =

M4maths Previous Puzzles

25 Mar 2010 x/y?

If x^y = 2^12 (1)

and y^(x-2) = 2^12 (2) then x/y =

OPtion

1) 6
2) 2.5
3) 1/6
4) 1.5
5) 2/3
6) 1/2
7) 2
8) 16/3
9) 3/16
10) 32

Solution

xy = 212 (1)

Equation (1) gives the following possibilities
x y xy

2 12 2^12

4 6 4^6 (1)

8 4 8^4 (2)

16 3 16^3 (3)

64 2 64^2 (4)

4096 1 4096^1 (5)

Only (2) case satisfies the second equation.

Correct Option: 7 Best Solution (8)

Dr.Dipin Singh   14 years AGO

x^y = 2^12

and y^(x-2) = 2^12 ..................... means x^y = y^(x-2)= 2^12 = 8^4= 4^6

so x=8, y=4, hence x/y =8/4=2...option 7

and y^(x-2) = 2^12

Like? Yes (1) | No   

S. Singh   14 years AGO

x=8 and y =4. Hence x/y =2

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HARMEET KAUR   14 years AGO

y=4......x=8.....x/y=2

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Aman   14 years AGO

x=8, y=4..... x/y =2

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ASHOK ROY   14 years AGO

2^12 can be written as 8^4 where from equation 1 x=8 and y = 4. Putting the values in equation 2 we get y^(x-2)=4^6= 2^12. So x/y=8/4=2

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Dr. Divya   14 years AGO

x^y = 2^12 = (2^3)^4 = 8^4

y^(x-2)= (2^2)^6 = 4^6 = 4^(8-2)

so x=8 and y =4

x/y=2

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Prerna   14 years AGO

x=8,y=4, x/y=2

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Achelal Sharma   14 years AGO

x^y=4096
y^(x-2)=4096

solving we get x=8
y=4

so x/y=2

Like? Yes (1) | No