What is ln(2x-(21)/x)<= 0 ?

The solution to ln(2x-(21)/x)<= 0 is -sqrt(21/2)<x<=-3\lor sqrt(21/2)<x<= 7/2

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ln(2x-(21)/x)<= 0

ln (2 x - \frac{21}{x}) \leq 0

- \frac{21}{2} < x \leq - 3 or \frac{21}{2} < x \leq \frac{7}{2}

Interval Notation

(- \frac{21}{2}, - 3] \cup (\frac{21}{2}, \frac{7}{2}]

Decimal Notation

- 3.24037 \dots < x \leq - 3 or 3.24037 \dots < x \leq 3.5

Solution steps

ln (2 x - \frac{21}{x}) \leq 0

Apply log rules

2 x - \frac{21}{x} \leq 1 and 2 x - \frac{21}{x} > 0

2 x - \frac{21}{x} \leq 1 and 2 x - \frac{21}{x} > 0 : - \frac{21}{2} < x \leq - 3 or \frac{21}{2} < x \leq \frac{7}{2}

- \frac{21}{2} < x \leq - 3 or \frac{21}{2} < x \leq \frac{7}{2}

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What is ln(2x-(21)/x)<= 0 ?
The solution to ln(2x-(21)/x)<= 0 is -sqrt(21/2)<x<=-3\lor sqrt(21/2)<x<= 7/2