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
Shubhanjay Varma , 10 Years ago
Grade 11
Algebra> If log2(x) + logx(2) = 10/3 = log2(y) + l...
1 AnswersVikas TU
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.
Approved Last Activity: 10 Years ago
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