What is log_{10}(x)(((2x+2/5))/((5(1-x))))>0 ?

The solution to log_{10}(x)(((2x+2/5))/((5(1-x))))>0 is No Solution

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log_{10}(x)(((2x+2/5))/((5(1-x))))>0

lo g_{10} (x) (\frac{( 2 x + \frac{2}{5} )}{( 5 ( 1 - x ) )}) > 0

No Solution

Solution steps

lo g_{10} (x) \frac{2 x + \frac{2}{5}}{5 ( 1 - x )} > 0

Simplify

lo g_{10} (x) \frac{2 x + \frac{2}{5}}{5 ( 1 - x )} : \frac{lo g _{10} ( x ) ( 10 x + 2 )}{25 ( 1 - x )}

\frac{lo g _{10} ( x ) ( 10 x + 2 )}{25 ( 1 - x )} > 0

Multiply both sides by

25

\frac{25 lo g _{10} ( x ) ( 10 x + 2 )}{25 ( 1 - x )} > 0 \cdot 25

Simplify

\frac{lo g _{10} ( x ) ( 10 x + 2 )}{1 - x} > 0

Factor

\frac{lo g _{10} ( x ) ( 10 x + 2 )}{1 - x} : \frac{2 lo g _{10} ( x ) ( 5 x + 1 )}{1 - x}

\frac{2 lo g _{10} ( x ) ( 5 x + 1 )}{1 - x} > 0

Divide both sides by

2

\frac{\frac{2 l o g _{10} ( x ) ( 5 x + 1 )}{1 - x}}{2} > \frac{0}{2}

Simplify

\frac{lo g _{10} ( x ) ( 5 x + 1 )}{1 - x} > 0

Identify the intervals

No Solution for x \in R

No Solution

lo g_{4} (x^{2} - 3 x + 2) > lo g_{4} (x^{2} - 5 x + 4)

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

x + 2 \geq x

\frac{3}{( 2 - x )} - 2 - x < 2

x - 5 - 9 - x > 1

What is log_{10}(x)(((2x+2/5))/((5(1-x))))>0 ?
The solution to log_{10}(x)(((2x+2/5))/((5(1-x))))>0 is No Solution