What is sqrt(log_{x)(2)*log_{2}(4-x)}>0 ?

The solution to sqrt(log_{x)(2)*log_{2}(4-x)}>0 is 1<x<3

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sqrt(log_{x)(2)*log_{2}(4-x)}>0

lo g_{x} (2) \cdot lo g_{2} (4 - x) > 0

1 < x < 3

Solution steps

lo g_{x} (2) lo g_{2} (4 - x) > 0

Square both sides

(lo g_{x} (2) lo g_{2} (4 - x))^{2} > 0^{2}

Simplify

\frac{ln ( 4 - x )}{ln ( x )} > 0

\frac{ln ( 4 - x )}{ln ( x )} > 0 : 1 < x < 3

1 < x < 3

Find singularity points

Find non-negative values for radicals:

1 < x \leq 3

Combine the intervals

1 < x < 3 and 1 < x \leq 3

Merge Overlapping Intervals

1 < x < 3

5 x - 3 < 2 x

\frac{x}{5} - 2 = 0

\frac{2 x}{3} = 6

9 = - 2 x^{2} + 3 x

37 + 57

What is sqrt(log_{x)(2)*log_{2}(4-x)}>0 ?
The solution to sqrt(log_{x)(2)*log_{2}(4-x)}>0 is 1<x<3