What is 2^{x/8}<= x ?

The solution to 2^{x/8}<= x is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{x/8}<= x

2^{\frac{x}{8}} \leq x

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Decimal Notation

x = 43.55926 \dots

Solution steps

2^{\frac{x}{8}} \leq x

Prepare

2^{\frac{x}{8}} \leq x

for Lambert form:

1 \leq x e^{- \frac{l n ( 2 ) x}{8}}

Rewrite the equation with

- \frac{ln ( 2 ) x}{8} = u

and

x = - \frac{8 u}{ln ( 2 )}

1 \leq (- \frac{8 u}{ln ( 2 )}) e^{u}

Rewrite

1 \leq (- \frac{8 u}{ln ( 2 )}) e^{u}

in Lambert form:

e^{u} u \leq - \frac{ln ( 2 )}{8}

Solve

e^{u} u \leq - \frac{ln ( 2 )}{8} : u = W_{- 1} (- \frac{ln ( 2 )}{8})

u = W_{- 1} (- \frac{ln ( 2 )}{8})

Substitute back

u = - \frac{ln ( 2 ) x}{8},

solve for

x

Solve

- \frac{ln ( 2 ) x}{8} = W_{- 1} (- \frac{ln ( 2 )}{8}) : x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

x^{2} + 6 x - 9 = 0

x^{2} - 7 x < 8

2^{x} = 3

9 x^{2} - 18 x + 8

\frac{x}{8} = \frac{8}{18}

What is 2^{x/8}<= x ?
The solution to 2^{x/8}<= x is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2))