If 2( log 2 x)2+x log 2 x=32, then

Question

If 2( log 2 x)2+x log 2 x=32, then (A) equation has two rational solutions. (B) equation has one rational and one irrational solutions. (C) product of all solutions is 1 . (D) product of all solutions is 2 √2.

Tardigrade Admin · Accepted Answer

Put log 2 x=y ⇒ x=2y ⇒ 2y2+2y2=32 ⇒ y = ± 2. So, x =4, (1/4)

Q. If $2^{(l o g_{2} x)^{2}} + x^{l o g_{2} x} = 32$ , then

equation has two rational solutions.

equation has one rational and one irrational solutions.

product of all solutions is 1 .

product of all solutions is $22$ .

Put $lo g_{2} x = y \Rightarrow x = 2^{y} \Rightarrow 2^{y^{2}} + 2^{y^{2}} = 32$
$\Rightarrow y = \pm 2$ . So, $x = 4, \frac{1}{4}$

Q. If 2(log2​x)2+xlog2​x=32, then