What is -4log_{5}(x)-5>= 3 ?

The solution to -4log_{5}(x)-5>= 3 is 0<x<= 1/25

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-4log_{5}(x)-5>= 3

- 4 lo g_{5} (x) - 5 \geq 3

0 < x \leq \frac{1}{25}

Interval Notation

(0, \frac{1}{25}]

Decimal Notation

0 < x \leq 0.04

Solution steps

- 4 lo g_{5} (x) - 5 \geq 3

Move

5

to the right side

- 4 lo g_{5} (x) \geq 8

Multiply both sides by

- 1

4 lo g_{5} (x) \leq - 8

Divide both sides by

4

lo g_{5} (x) \leq - 2

Apply log rules

x \leq \frac{1}{25} and x > 0

Merge Overlapping Intervals

0 < x \leq \frac{1}{25}

- 3 (3)^{2} + 2 (3) + 1

4 x = \frac{5}{2} x - 4

∣ n ∣ + 4 < 12

x + x^{2} + 1 > 0

x^{2} + 3 x - 10 > 0