en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^x+x-3<0

Solution

2^{x} + x - 3 < 0

Solution

x < 1

+1

Interval Notation

(- \infty, 1)

Solution steps

2^{x} + x - 3 < 0

Move

x

to the right side

2^{x} - 3 < - x

Move

3

to the right side

2^{x} < - x + 3

Prepare

2^{x} < - x + 3

for Lambert form:

1 < (- x + 3) e^{- l n (2) x}

Rewrite the equation with

(- x + 3) ln (2) = u

and

x = - \frac{u - 3 ln ( 2 )}{ln ( 2 )}

1 < (- (- \frac{u - 3 ln ( 2 )}{ln ( 2 )}) + 3) e^{- l n (2) (- \frac{u - 3 l n ( 2 )}{l n ( 2 )})}

Simplify

1 < e^{u - 3 l n (2)} (\frac{u - 3 ln ( 2 )}{ln ( 2 )} + 3)

Rewrite

1 < e^{u - 3 l n (2)} (\frac{u - 3 ln ( 2 )}{ln ( 2 )} + 3)

in Lambert form:

e^{u} u > 8 ln (2)

Solve

e^{u} u > 8 ln (2) : u > 2 ln (2)

u > 2 ln (2)

Substitute back

(- x + 3) ln (2) = u,

solve for

x

Solve

(- x + 3) ln (2) > 2 ln (2) : x < 1

x < 1

Popular Examples

2^{x} > - x + 3

(2^n)/((2^{n+2)-3)}< 1/4

\frac{2 ^{n}}{( 2 ^{n + 2} - 3 )} < \frac{1}{4}

((4^x+2))/9 <2^{x-1}

\frac{( 4 ^{x} + 2 )}{9} < 2^{x - 1}

0. 3^{x} < 1 0^{- 4}

2^{n} - 2 \geq 4

Frequently Asked Questions (FAQ)

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