Question

log2^x+logx^2=(10/3)=log2^y+logy^2 then x+y=

Answer 1

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.