The given equation is x^(3/4(log_2x)2+log_2x−5/4)=sqrt2 I took log_2x = t and then rewrote the given equation as x^(3t^2+4t−5)=sqrt2 But I don't know what to do after this. How will I find the nature and no. of roots?

Kaila Branch 2022-09-24 Answered
no. and nature of roots of x 3 4 ( log 2 x ) 2 + log 2 x 5 4 = 2
The given equation is
x 3 4 ( log 2 x ) 2 + log 2 x 5 4 = 2
I took log 2 x
and then rewrote the given equation as
x 3 t 2 + 4 t 5 = 2
But I don't know what to do after this. How will I find the nature and no. of roots?
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Answers (2)

Bridger Hall
Answered 2022-09-25 Author has 7 answers
x 3 4 ( log 2 x ) 2 + log 2 x 5 4 = 2
log 2 x 3 4 ( log 2 x ) 2 + log 2 x 5 4 = log 2 2
log 2 x ( 3 4 ( log 2 x ) 2 + log 2 x 5 4 ) = 1 2
t = log 2 x
3 t 3 + 4 t 2 5 t 2 = 0
t 1 = 1.
Can you finish?
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Darius Miles
Answered 2022-09-26 Author has 3 answers
I'd try to take log 2 of the whole expression and the solve with respect to t = log 2 x
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