en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^x+x=11

Solution

2^{x} + x = 11

Solution

x = 3

Solution steps

2^{x} + x = 11

Prepare

2^{x} + x = 11

for Lambert form:

1 = (11 - x) e^{- l n (2) x}

Rewrite the equation with

(- x + 11) ln (2) = u

and

x = - \frac{u - 11 ln ( 2 )}{ln ( 2 )}

1 = (11 - (- \frac{u - 11 ln ( 2 )}{ln ( 2 )})) e^{- l n (2) (- \frac{u - 11 l n ( 2 )}{l n ( 2 )})}

Simplify

1 = e^{u - 11 l n (2)} (11 + \frac{u - 11 ln ( 2 )}{ln ( 2 )})

Rewrite

1 = e^{u - 11 l n (2)} (11 + \frac{u - 11 ln ( 2 )}{ln ( 2 )})

in Lambert form:

e^{u} u = 2048 ln (2)

Solve

e^{u} u = 2048 ln (2) : u = 8 ln (2)

u = 8 ln (2)

Substitute back

u = (- x + 11) ln (2),

solve for

x

Solve

(- x + 11) ln (2) = 8 ln (2) : x = 3

x = 3

Popular Examples

10^{-x}=5^{x-1}

1 0^{- x} = 5^{x - 1}

solvefor y,x^y+e^x=a solve for

y, x^{y} + e^{x} = a

3^{2x+2}+17*3^x=2

3^{2 x + 2} + 17 \cdot 3^{x} = 2

9^x-90*3^x+729=0

9^{x} - 90 \cdot 3^{x} + 729 = 0

5 e^{x} = 1

Frequently Asked Questions (FAQ)

What is the answer to 2^x+x=11 ?
The answer to 2^x+x=11 is x=3
Solve for x: 2^x+x=11
The solution is x=3