en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^x=27

Solution

x^{x} = 27

Solution

x = 3

Solution steps

x^{x} = 27

Prepare

x^{x} = 27

for Lambert form:

x e^{- \frac{3 l n ( 3 )}{x}} = 1

Rewrite the equation with

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

and

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

(\frac{3 ln ( 3 )}{u}) e^{- u} = 1

Rewrite

(\frac{3 ln ( 3 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 3 ln (3)

Solve

u e^{u} = 3 ln (3) : u = ln (3)

Verify Solutions:

u = ln (3)

True

The solution is

u = ln (3)

Substitute back

u = \frac{3 ln ( 3 )}{x},

solve for

x

Solve

\frac{3 ln ( 3 )}{x} = ln (3) : x = 3

x = 3

Popular Examples

9^{x} = 3^{x} - 4

solvefor k,n-2=3^k solve for

k, n - 2 = 3^{k}

(27^{27})^x=(3^{27})^{17}

(2 7^{27})^{x} = (3^{27})^{17}

327 = 3^{k}

17^{-3x}=9^{x+9}

1 7^{- 3 x} = 9^{x + 9}

Frequently Asked Questions (FAQ)

What is the answer to x^x=27 ?
The answer to x^x=27 is x=3
Solve for x: x^x=27
The solution is x=3