What is log^2_{2}(x)-3log_{2}(x)+2>= 0 ?

The solution to log^2_{2}(x)-3log_{2}(x)+2>= 0 is 0 = 4

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log^2_{2}(x)-3log_{2}(x)+2>= 0

lo g_{2}^{2} (x) - 3 lo g_{2} (x) + 2 \geq 0

0 < x \leq 2 or x \geq 4

Interval Notation

(0, 2] \cup [4, \infty)

Solution steps

lo g_{2}^{2} (x) - 3 lo g_{2} (x) + 2 \geq 0

Let

u = lo g_{2} (x)

u^{2} - 3 u + 2 \geq 0

u^{2} - 3 u + 2 \geq 0 : u \leq 1 or u \geq 2

u \leq 1 or u \geq 2

Substitute back

u = lo g_{2} (x)

lo g_{2} (x) \leq 1 or lo g_{2} (x) \geq 2

lo g_{2} (x) \leq 1 : 0 < x \leq 2

lo g_{2} (x) \geq 2 : x \geq 4

Combine the intervals

0 < x \leq 2 or x \geq 4

500 a^{3} + 4

x^{2} - 9 x + 20 > 0

y^{3} - 1

\frac{x}{2} = 6.5

a^{\frac{3}{2}}

What is log^2_{2}(x)-3log_{2}(x)+2>= 0 ?
The solution to log^2_{2}(x)-3log_{2}(x)+2>= 0 is 0<x<= 2\lor x>= 4