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If log2(x) + logx(2) = 10/3 = log2(y) + logy(2) and x is not = y, find x+y

If log2(x) + logx(2) = 10/3 = log2(y) + logy(2) and x is not = y, find x+y

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Take  log2(x) + logx(2) = 10/3 first,
this can be written as:
 1/logx(2) + logx(2) = 10/3
let logx(2) = t
then it becomes a quadratic,
as:
3t^2 – 10t + 3 = 0
its roots are =>
(3t – 1) (t – 3) = 0
 
t = 1/3  and  t  = 3
             or
logx(2) = 1/3  and  logx(2) = 3
x = 2^(1/3)     and    x = 2^3 = 8
 
Now same eqn. will becomes in y form.
.i.e.
y = 2^(1/3)     and    y = 2^3 = 8
 
Now when x is not equal to the sum x+y =>
x = 2^(1/3)  and y = 2^3 = 8
Hence,
x + y = 2^(1/3) + 2^3 is the answer.

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