en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

0 < x < 1

+1

Interval Notation

(0, 1)

Solution steps

2^{x} + 2^{- x + 1} - 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

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

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

((2^{x-1}-1))/((2^{x+1)+1)}<2

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

2^{3 - 8 x} > 1

(2^x+1)(3^x+1)(4^x+1)<0

(2^{x} + 1) (3^{x} + 1) (4^{x} + 1) < 0

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

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

Frequently Asked Questions (FAQ)

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