The equation, log 2(2 x2)+ log 2 x ⋅ x log x( log 2 x+1)+(1/2) log 4 2 x4+2-3 log ν 2( log 2 x)=1 has :

Question

The equation, log 2(2 x2)+ log 2 x ⋅ x log x( log 2 x+1)+(1/2) log 4 2 x4+2-3 log ν 2( log 2 x)=1 has : (A) exactly one real solution (B) two real solutions (C) 3 real solutions (D) no solution.

Tardigrade Admin · Accepted Answer

y3+3 y2+3 y+1=1 text where y= log 2 x ⇒ y(y2+3 y+3)=0 ⇒ x=0 text (rejected) ; y2+3 y+3 text (complex roots)

Q. The equation, $lo g_{2} (2 x^{2}) + lo g_{2} x \cdot x^{l o g_{x} (l o g_{2} x + 1)} + \frac{1}{2} lo g_{4}^{2} x^{4} + 2^{- 3 l o g_{ν 2} (l o g_{2} x)} = 1$ has :

exactly one real solution

two real solutions

3 real solutions

no solution.

$y^{3} + 3 y^{2} + 3 y + 1 = 1 where y = lo g_{2} x \Rightarrow y (y^{2} + 3 y + 3) = 0$
$\Rightarrow x = 0 (rejected); y^{2} + 3 y + 3 (complex roots)$

Q. The equation, log2​(2x2)+log2​x⋅xlogx​(log2​x+1)+21​log4​2x4+2−3logν2​(log2​x)=1 has :