en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-1<= (1/3)^x<2

Solution

- 1 \leq (\frac{1}{3})^{x} < 2

Solution

x > - lo g_{3} (2)

+2

Interval Notation

(- lo g_{3} (2), \infty)

Decimal Notation

x > - 0.63092 \dots

Solution steps

- 1 \leq (\frac{1}{3})^{x} < 2

If

a \leq u < b

then

a \leq u and u < b

- 1 \leq (\frac{1}{3})^{x} and (\frac{1}{3})^{x} < 2

- 1 \leq (\frac{1}{3})^{x} :

True for all

x

(\frac{1}{3})^{x} < 2 : x > - lo g_{3} (2)

Combine the intervals

True for all x and x > - lo g_{3} (2)

Merge Overlapping Intervals

x > - lo g_{3} (2)

Popular Examples

-1<= x/((x+2))<= 3

- 1 \leq \frac{x}{( x + 2 )} \leq 3

5x-2<10x+8<2x-8

5 x - 2 < 10 x + 8 < 2 x - 8

x - 1 < x + 3 < 5

0 < ∣ 3 x + 1 ∣ < \frac{1}{3}

- 2 < 8 - 2 x < - 1

Frequently Asked Questions (FAQ)

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