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Popular >

2^x+2^{1-x}-3<0

Solution

2^{x} + 2^{1 - x} - 3 < 0

Solution

0 < x < 1

+1

Interval Notation

(0, 1)

Solution steps

2^{x} + 2^{1 - x} - 3 < 0

Apply exponent rules

(2^{x})^{2} + 2 - 3 \cdot 2^{x} < 0

Let

u = 2^{x}

u^{2} + 2 - 3 u < 0

u^{2} + 2 - 3 u < 0 : 1 < u < 2

1 < u < 2

Substitute back

u = 2^{x}

1 < 2^{x} < 2

If

a < u < b

then

a < u and u < b

1 < 2^{x} and 2^{x} < 2

1 < 2^{x} : x > 0

2^{x} < 2 : x < 1

Combine the intervals

x > 0 and x < 1

Merge Overlapping Intervals

0 < x < 1

Popular Examples

x(2^x-1)(3^x-9)(x-3)<0

x (2^{x} - 1) (3^{x} - 9) (x - 3) < 0

(((3^x-1)*(x-1)^3))/((x*(x-2)^5))<= 0

\frac{( ( 3 ^{x} - 1 ) \cdot ( x - 1 ) ^{3} )}{( x \cdot ( x - 2 ) ^{5} )} \leq 0

(0.3)^{2x^2-3x+6}<0.00243

(0.3)^{2 x^{2} - 3 x + 6} < 0.00243

e^{x} > - 1

2^{3x+5}>4^{2x+4}

2^{3 x + 5} > 4^{2 x + 4}

Frequently Asked Questions (FAQ)

What is 2^x+2^{1-x}-3<0 ?
The solution to 2^x+2^{1-x}-3<0 is 0<x<1