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

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

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

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

5 < x \leq \frac{1}{5 ^{\frac{3}{4}}} + 5

Interval Notation

(5, \frac{1}{5 ^{\frac{3}{4}}} + 5]

Decimal Notation

5 < x \leq 5.29906 \dots

Solution steps

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

Multiply both sides by

- 1

(reverse the inequality)

(- 4 lo g_{5} (x - 5)) (- 1) \leq 3 (- 1)

Refine

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

Divide both sides by

4

\frac{4 lo g _{5} ( x - 5 )}{4} \leq \frac{- 3}{4}

Simplify

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

Apply log rules

x - 5 \leq \frac{1}{5 ^{\frac{3}{4}}} and x - 5 > 0

x - 5 \leq \frac{1}{5 ^{\frac{3}{4}}} and x - 5 > 0 : 5 < x \leq \frac{1}{5 ^{\frac{3}{4}}} + 5

5 < x \leq \frac{1}{5 ^{\frac{3}{4}}} + 5

\frac{n !}{( n - 2 ) !}

- \frac{16}{2025} x^{2} + \frac{9}{5} x + 1.5 = 0

2 x + 3 \cdot 8 = 12

x^{2} - 60 x + 2 = 0

3 x - 2 x^{2} = 0

What is -4log_{5}(x-5)>= 3 ?
The solution to -4log_{5}(x-5)>= 3 is 5<x<= 1/(5^{3/4)}+5