What is sqrt(log_{x)(x)}<2 ?

The solution to sqrt(log_{x)(x)} 1

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sqrt(log_{x)(x)}<2

lo g_{x} (x) < 2

0 < x < 1 or x > 1

Interval Notation

(0, 1) \cup (1, \infty)

Solution steps

lo g_{x} (x) < 2

Square both sides

(lo g_{x} (x))^{2} < 2^{2}

Simplify

1 < 4

Therefore, the solution is

True

Find singularity points

Find non-negative values for radicals:

0 < x < 1 or x > 1

Combine the intervals

True and (0 < x < 1 or x > 1)

Merge Overlapping Intervals

0 < x < 1 or x > 1

x - 1 > 3 - x

x^{2} - 4 x > x - 2

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > (2)^{\frac{1}{2}}

x - 2 + 2 \leq x

x - 3 < x - 2

What is sqrt(log_{x)(x)}<2 ?
The solution to sqrt(log_{x)(x)}<2 is 0<x<1\lor x>1