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Popular >

(4^x)^2-4<0

Solution

(4^{x})^{2} - 4 < 0

Solution

x < \frac{1}{2}

+2

Interval Notation

(- \infty, \frac{1}{2})

Decimal Notation

x < 0.5

Solution steps

(4^{x})^{2} - 4 < 0

Move

4

to the right side

(4^{x})^{2} < 4

For

u^{n} < a

, if

n

is even then

- 4 < 4^{x} < 4

4 = 2

- 2 < 4^{x} < 2

If

a < u < b

then

a < u and u < b

- 2 < 4^{x} and 4^{x} < 2

- 2 < 4^{x} :

True for all

x

4^{x} < 2 : x < \frac{1}{2}

Combine the intervals

True for all x and x < \frac{1}{2}

Merge Overlapping Intervals

x < \frac{1}{2}

Popular Examples

(1/16)^x<(1/2)^{x+3}

(\frac{1}{16})^{x} < (\frac{1}{2})^{x + 3}

(2^x-3)(2^x-5)<= 15

(2^{x} - 3) (2^{x} - 5) \leq 15

(3^{x})^{2} < 81

(3^{x/2})^{x-1}>= (3/9)^{x-3}

(3^{\frac{x}{2}})^{x - 1} \geq (\frac{3}{9})^{x - 3}

3^{x} \geq 5

Frequently Asked Questions (FAQ)

What is (4^x)^2-4<0 ?
The solution to (4^x)^2-4<0 is x< 1/2