Question

Solve for x:

Answer 1

\[\sqrt{\log_{2}x-1}-1/2\log_{2}x^{3}+2>0\]
Ans. x belongs to [2,4)

Answer 2

let y=log2(x) and solve for y

Answer 3

lol wow another long one..hmm

Answer 4

anyone solving ??

Answer 5

@nitz

Answer 6

@lgbasallote Do you know the solution to it??

Answer 7

is this the inequality: \(\large \sqrt{log_2x-1}-\frac{1}{2}log_2x^3+2>0 \)

Answer 8

yes

Answer 9

\(\large \sqrt{log_2x-1}-\frac{1}{2}log_2x^3+2>0 \)
\(\large \sqrt{log_2x-1}-\frac{3}{2}log_2x+2>0 \)
\(\large \sqrt{log_2x-1}>\frac{3}{2}log_2x-2 \)
\(\large log_2x-1>(\frac{3}{2}log_2x-2)^2 \)

looks like a quadratic form from here... can you take it from here by using what @mukushla said?

Answer 10

ok

Answer 11

that inequality will look like this:

\(\large y-1>(\frac{3}{2}y-2)^2 \)

Answer 12

thanks

Answer 13

yw...:)