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Popular >

|3^x-5|<1

Solution

∣ 3^{x} - 5 ∣ < 1

Solution

2 lo g_{3} (2) < x < lo g_{3} (6)

+2

Interval Notation

(2 lo g_{3} (2), lo g_{3} (6))

Decimal Notation

1.26185 \dots < x < 1.63092 \dots

Solution steps

∣ 3^{x} - 5 ∣ < 1

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 1 < 3^{x} - 5 < 1

3^{x} - 5 > - 1 and 3^{x} - 5 < 1

x > 2 lo g_{3} (2) and x < lo g_{3} (6)

Merge Overlapping Intervals

2 lo g_{3} (2) < x < lo g_{3} (6)

Popular Examples

x^{2} - 3 ∣ x ∣ - 10 < 0

∣ 3 t - 4 ∣ < 8

∣ 6 x - 12 ∣ < ∣ 2 - x ∣

|(3x)/((x^2-4))|<= 1

\frac{3 x}{( x ^{2} - 4 )} \leq 1

|x^2-9|+|x^2-1|>8

x^{2} - 9 + x^{2} - 1 > 8

Frequently Asked Questions (FAQ)

What is |3^x-5|<1 ?
The solution to |3^x-5|<1 is 2log_{3}(2)<x<log_{3}(6)