What is x/((log_{1/2)(2x+3))}>0 ?

The solution to x/((log_{1/2)(2x+3))}>0 is -1<x<0

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x/((log_{1/2)(2x+3))}>0

\frac{x}{( lo g _{\frac{1}{2}} ( 2 x + 3 ) )} > 0

- 1 < x < 0

Interval Notation

(- 1, 0)

Solution steps

\frac{x}{lo g _{\frac{1}{2}} ( 2 x + 3 )} > 0

Identify the intervals

- 1 < x < 0

x \cdot ln (x^{3}) < 0

lo g_{10} (2 - x) > lo g_{10} (1 + 2 x)

lo g_{2} (1 - 2 x) < lo g_{2} (x + 1)

lo g_{\frac{1}{2}} (2 x + 3) > 0

lo g_{3} (x + 1) + lo g_{3} (x + 7) \geq 3

What is x/((log_{1/2)(2x+3))}>0 ?
The solution to x/((log_{1/2)(2x+3))}>0 is -1<x<0