Question

If 3^x = 4^y =12^xy, then find x+y.

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Answer 1

Answer:

3^x=4^y =12^xy

or x.log3 =y.log4 = x.y.log12

or x.log3=x.y.log12 => 1= y.log12/log3.

y=(log3)/(log12)……………..(1)

y.log4=x.y.log12 => 1 =x.log12/log4

x=(log4)/(log12)……………..(2)

Adding eqn.(1) and(2)

x+y=1/log12.[log4+log3]

x+y =(log4×3)/(log12)=log12/log12 = 1 .

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Answer 2

Explanation:

3^x=4^y =12^xy

or x.log3 =y.log4 = x.y.log12

or x.log3=x.y.log12 => 1= y.log12/log3.

y=(log3)/(log12)……………..(1)

y.log4=x.y.log12 => 1 =x.log12/log4

x=(log4)/(log12)……………..(2)

Adding eqn.(1) and(2)

x+y=1/log12.[log4+log3]

x+y =(log4×3)/(log12)=log12/log12 = 1 .